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30 I MASTERMND CHAPTERWISE QUESTION BANK, 015., , cos, , 2, , snsequalt, , Principal value of cosec, , b., , a, , a., , 4, , So, the value of, , 8, , tan'(-)+sec(-2)-cosec, , Sol (a) Principal value of cos, , ), , and principal value of sin, ., , Principal value of cos, , 018. cos +2sin 4tansequalto:, , (2, , d. -, , 4, , st"sequalto:, , +cos, , d.6, , Sol, , (cos 2sn (4ta, , a19. Domain of cos [x] (where [] denotes (G.1.F.) is:, , Sol (b) Let tan'() =0=tan =1= tan, , a.(-12), , b.[-12), , c(-12), , d. None of these, , SoL (b) Clearly, -1s (x] s1, -1sx<2, , Principal value of tan () is, , xe[-12), 20. Range of fix) = sinx + tanx+ secx is:, , d. None of these, , Sol (c) Givenflx)= sin x +tan x + sec'x, , Principal value ofcos, , Domain ofsinx =[-1), Domain of tan'x = (-, ), , Similarly:principal value ofsin|, , Domain ofsecx =(- )-(-1), , .The value of tan () +cos, , Domain offl)=(-1)nll-- -)nl(--))-(-1)), ={-1), Now.f(-1)=sin(-1) + tan(-1)+ sec(-, , a 17., , tan)+ se"-)-cosec, , sequalto:, , and, , 0, , d.0, , SoL (d) Let tan(-3)=a, , f)=sin () +tan ()+sec (), , Rangeofflx)-, , tan a =-V3 =- tan, , a21. Which of the following, , principal value branch o, (NCERTEXEMPLA, , is the, , cos x?, , b. (0 7), , Principal value oftan(-V3) is, , Letsec'(-2)=B-~secß, , =, , d(0 )-, , -2- -sec, , SoL (c) Principal value branch of cos x is [0 x), , a 22. Which of the following is the principal value branch o, , cosecx?, , Principal value ofsee'(-2), Letcose=r=cosecy, , a, , (NCERTEXEMPLAR=, , (0 )-, , is, , cosee, , SoL, , (d) Principal value branch ofcosec, , *s-0

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32, , MASTERMND CHAPTERWISE QUESTION BANK, :cos-x) = T - cos, , -2x+47-3, , n-, , 12, , 034. The principalvalue ofsin i :, , Q39. The value of cos"]*sin, , 4T, d. None of these, , b. 0, , Sol (b)Letsin, , sal(olcorsin2, 3, , sin x, , (x,y,z), sinx+ siny +sindz =is, , Q 40. The number of triplets, , sin x =sin, , satisfies the, , equation, , 2, , b. 2, , a.1, Sol, , (a) We have,sin, , 0 35. The principal value of cot(-1) is:, 3T, , d. infinite, , C.0, x +, , sin"'y +, , sin'z=, , ssin'xsssinys, , d. None of these, , 4, , Sol (c)Clearly.cot(-1) n-cot (), , ssis, , and, , -cot cot, , .The above condition will, , satisfy, if, , sin'x =siny=sin'z, , =, , X =y=Z =l, 3n, , Q41. The value ofsin| c o s i, , (NCERTEXEMPLAR), , 7t, , 0 36. The value of cos cos, , a, 0, ol(0)sico)]-inco, , b.-1, , a.1, c.0, , d. None of these, , SoL, , -sinsn, f:cos(-x)=r -cosx]1, = COST = -1, , -cos-, , -1s2x -1s10s2xs2 »0Sxs1, =, , |, , a, , tan(-x)= tan" x andcos(-x), -, , sin, , a 38. The value of sin co, , b. 1, d. None of these, , b.[-11), , (1.2), , Sol (a) We know, , sin-tan + t-cos, , -sin, , c(-1), , cos (2x -1) Sn, , defined by flx) sin x-1, 43. The domain ofthe function, (NCERTEXEMPLAR), is:, , d. None of these, , Sol (o)sin tan-)+cos, , (a), , We know, 0 s, , (NCERTEXEMPLAR), d. (0 ), , Domain ofcos (2x - 1)=[0.1), , b.-, , C.O, , b.(-1, , a. [0.1), Sol, , 37. The value ofsin tan-)+cos, a.1, , Q42. The domain ofthefunction cos2x-1)is:, , c, , [0.1), , d. None of these, , ssinx-1s, , -1sx-1s1»0sx-1s1 1sxs2, =, , r, , -, , cos x), , Domain off(x) is ([1. 2], , Q44. The value of cos, , is equal to:, , (NCERTEXEMPLAR)

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| Class 12I Term-1, , Mathematics, , o46 cos cosequalto, , (NCERTEXERCISE), , ) cos coscoscos2-, , s, , 51. The principal value ofsin, , where., , d. None of these, , (a) sins to be written as sin a, , Sol, , fcos (2-0) =cos e), , o6., , |33, , The valueofsin (cos, b, , (NCERTEXEMPLAR), , 5, , so(0)sin"|cos, , sintos B, , Q47. The principal value of the expressioncos [cos(-680°)], , is:, , -aan-)}, , d-0, , ()), -, , ses, , where,, , 52. The value ofsinsini:, , a, , 4T, , c, , Sol, , (NCERTEXEMPLAR), , = sin, , b, , 9, , a53. The value, , Sol (a)cos (cos (680°)) =cos (cos (720°- 40° )], , cos cos(-40°)) =cos"(cos(40 )-, , a, , cos(sin:, , ofsin (cos, , 17, , 40°=, , d. None of these, , 048. If cosx+ cosy + cosz = 3n, then xy + y2 + 2x is, , Sol (b)sin?, , equal to:, , b.0, d.-1, , a.-3, 3, , l-cocos1-rar, , Sol (c) We know that. 0 scosx sn, cosx+ cos"y + cos z =3x, cosx =cosy =cos z =n, , a54. The value of sin, , X=y=Z=-1, , -(-G)2:, , (CBSE 2020), , xy + yZ t ZX =3, , 8, , 49. The value of tan, , B, Sol, , 12, , (c) Given. sin"|, The principal value ofsin xi, , tan-tantan tan(-, , Since,, , : tan (-x)=- tan x), , Now, O50. The principal value of, , sin|sin, , 4, , d. None of these, , n-anax, in-in, -sin' sin, , sin (-9)=-sine), (sin (2+8) =sin@), , -sin (o)=sin (-9)], , sin (sin )- veei

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Mathematics, , a6. The principal value of sin, , 071. Statement-1: The value, , | Class 12, , Term-1, , | 35, , ofsin tan (-V3)+cos, , is 1., , d. None of these, , Statement-ll:tan"(-x)= -tanx, , 5ol, , cos(-x)= cosx., , and, , Sol()sin tan(-)+ cos|, , a6. The principal value of sin " sin, d-, , s(aan-ssn, Q6. The value, , of tan, , sin-tan'3+n-cos, , inn, , (sec" 2)+ cot (cosec'is:, , a.5, c.13, , Thus, Statement-l is true but Statement-l is false, , (NCERTEXEMPLAR), , .11, , 072., , .15, , 2, , solutions., , sol (b)tan(sec 2)+ cot (cosec-3), =, , Statement-1:/f2(sin1x) -5(sinx)+2=Qthenxhas, , sec (sec2) -1+ cosec(cosec 3)-1, , 22x1+3 -2=11, , Statement-ll:sin (sin x)= x, if, Sol. (d)2(sin"x)-5(sin x)+2 =0, sin'x=tY25-16, , 069. tan, , 4, , b.1, , a.sol, , lo)tan, , sin'x=sin'x=2, , d, , is, , Xsin, , sin, =, , only solution, , ssin'xs, sin'x=2 is not possible), , tan(-)= tan'(), -, , = - tan'tan-, , . Statement-l is false., , a73. Statement-l: Range of expression, , 70. Iftan (secx)= sin| cos, , a, , b., , 5, , then xis equalto:, , 3, , ftx)-sin x+osx+2tan xis, , d. None of these, , Statement-ll: Range should be calculated for x e-1,11, , Sol, , Sol (a) We have,, , fx)= sin'x +cosx+2 tanx, , For domain ofsinx and cos x. -1s xsi, and domain of tan x, x eR, , tan(se)-sincos, se(se')-1--cocos, , Domain of f(x)=(-1.1), fx)-+2 tanx, , Clearly, , staxs 4, , xe[-1, , Now, as, , -1-14, -1, , x=, , (d), , 0sfx)s, Range of f(x) = {0 1], , Hence. Statement-l is false and Statement- is true., , 3, , a74. Statement-1:, , Assertion and Reason Type Questions, , Directions (Q. Nos. 71-74): In the following questions, a statement, of Assertion (Statement-1) is followed by a statement of Reason, (Statement-l). Mark the corect choice as, , a. Statement I is true, Statement ll is true: Statement I is a, correct explanation for Statement, b. Statement I is true. Statement ll is true: Statement ll is, , fa e-, , sin (sina)+cos, , (cosa) =a, Statement-ll: If a e 0 , then sin(sina) =a and, cos(cosa) = -a, Sol, , (a) sin (sin x), , =, , x,, , -SxS, , cos (cos x)= -x, T SX s0, , fae0thensinr'(sina) +cos"(cosa), , not a correct explanation for Statement I, , . Statement I is true, Statement l is false, d. Statement I is false, Statement, , is true, , :.Statement- is true and Statement-llis correct explanation, of Statement-

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36, , MASTERND CHAPTERWISE OUESrnoN BANK, Case Study Based, , QUESTIONS, , 03. 40RP=0=, , Case Stud1, , b. tan (2), , a tan, , d.tan), , cta, SoL, , C, , =60 metres, 240-60 =180metres, OR PR-OP =, PR=240 metres, , and OP, , Now, in right AQOR,, , 00 60 3, , tanOR, , 180, , tan, Two persons on either side of a temple of 60/3 metres, , height observes its top at the angles of elevation 0 and, , respectively (as shown in the given figure). The distance, , So,, , between the two persons is 240 metres and the distance, between the first person P and the temple is 60 metres., , option (c) is correct., , 04. POR=, , Based on the above information, give the answer of the, , following questions:, 01. LRPQ=0, , as, , ), , Sol In, , cat) d, , +0+ PQR =180°, , T!P-internal, , Sol Given that,, , Height, , of the, , temple. O0 =603, , =180°, APQR. LRPQ+ 2QRP + PQR, , Sum ofall, , metres, , angles ofa triangle is equal to 180., , LPQR =180, sin (sin 60)+ tan"(tan 30°)+ POR =180, , 603 m, , 60°+30+ PQR =180, R, , TR!CKDistance between two persons, PR =240 metress, the, and the distance between the first person Pand, , temple. OP =60 metres, Now, in right aQ0P,, , 00 60 3, , tan gP60, , sin ein)-6 i,e, tan tan 8)- if,ee, , tan 3=tan 60°, , POR 180°-90°90, , 0 60, , POR-90 T80, , sin=sin60°»sin, , Now, , So, option (c) is correct., , Q5., , aR, , So. option (d) is correct, , b.R.(0 x), , 02. 4RP=0=, , SolL, , Domain and Range of tan, , acos, , b cos, , cR-(-19(0)-, , ccos, , dcos, , dR-(-11, , Now.cos 8, , =, , cos, , 60°, , cos6, , -cos, So. option (a) is correct., , =, , -0, , Sol Domain of tan x is R, and, , Range of tan" x, , is-, , So, option (a) is correct, , x, , =

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Mathematics Class12, , Case Study 2, , value of an inverse, trigonometric function which lies, its, in Principal value branch is, called the, , The, , that inverse trigonometric function., When we refer to the function, , function, , whose domain, , is, , range, , The branch with, , is, , value branch., Based on the above, , SoL, , cot-co, , Principal value of, , sin, we take, -LI) and range is, called the, , it, , as, , the, cot cot, , Principal, , information, give the answer of the, following questions:, , So, option (b6) is correct., , -Common/!ErrorWithout knowing the range of cotx, students solve this|, question and get the wrong answer, , 01. Principal value of sin, , y, , eg, cot y=cot, d., , SoL, , --in, , while, y=-e(0,), as. Principalvalue ofcos, , sin sin, So. option (b) is correct., 02, , ., , a, , Principal value oftanWI)is:, , TR!CKS-, , s:, , 4, , SolL cos-, , cos-cos, , anr'-)- tantan, , =cos cos, So, option (c) is correct., , Range of tanx is, Range ofcotx is (0,7)., , So, option (a) is correct., , 03, , Principalvalue ofcos i, , Case Study3, The value of an inverse trigonometric function which lies, in its principal value branch is called the principal value of, that inverse trigonometric function., , Forexample: sinsin, Based on the above information, give the answer of the, , following questions:, a1. The value of, , Sol cos, , sin sin, b, , a. T, , SoL sin, , -coscos, , sinco' co, , So, option (¢) is correct, 4, , Term-1| 37, , Principal value of, , cot|, So., , option (a) is correct

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38, , MASTER MIND CHAPTERWISE OuESTION BANK, Q2. The value, of sin, , Sol. tant, , tan, So. option (a) is correct., , Sol sin, So., , 03., , hr'sin, , 5. The value ofsin, , option (a) is correct., , sin sinis equal, , Sol sin', , sin, , a, , to:, , sin sin- 4T, , So. option (c) is correct., , Q4., , Sol sin, , tan tanis equal to:, , 2, 6, , So, option (c) is correct., , tan tan