Page 1 : Chapter, , recipi, . Ifcos (sin-* 5 roo? | =0, then xis equal to:, , INCERT Exemplar], di, @ = ) =, (9 (dy 1, , . Which of the following corresponds to the principal, value branch of tan“! x?, , {(_uT ad, @ [-7] w [-34], oo, @ (-$3]-@ = @ Om, , . The principal value branch of sec" x is:, , 0 Sam ow wad, , (©) (On) (d), , , , ae, Fa, , . The principal value of the expression cos [cos, - 680°] is :, , , , , , , , 20 -2n, (a) > (b) “|, 34n T, (c) es (d) i, x, © + @ Vee, x z, . The domain of sin! 2x is:, @ [0.1] ) E41, © [-34] @) 12,2], , . The principal value of sin, , 2n, (a) =a (b), , © = (), , , , Inverse Trigonometric, , Functions, , 8. The domain of y= cos (x? - 4) is:, (a) [3,5], (6) [0], (9 E¥5,-Vlaes5,31, , (@) [-V3,- V8] U[v3, V5], , , , 9. The domain of the function defined by, fe) = sin x + cos xis:, (a) [-L1] (b) [-1,7+1], () (—%, %) (d) 6, 10. The value of sin [2 sin“ (0.6)] is:, (a) 48 (b) -96, () 12 (d) sin12, 1. The value of tan }cos’t ———, { V2, 29 29, @ 5 5, ¥3 3, ae Ey, © 9 35, , 2 a, 12. If cot Tse] =0, the value of sin @ is:, , , , V26 a, OF ” Be, , NS 5, (c) Pe (d) oe, , 13. Ifa<2sin 1 x+cos4x< f, then:, , =—s po, ame,, , (b) a=0, p=, _7~™ p_ 3a, angie ys, (d) a=0,B=27, 14. The value of tan? (sec! 2) + cot? (cosec™ 3) is:, (a) 5 (b) 1, () 2B (d) 15, , 15. The value of tan oS] lites, |

Page 2 : 16., , 1:, , 18., , 19., , 20., , 21., , 22., , 3+v5, , , , , , , , , , , , b) —— 23., (@) 3 (b) 3, -3+V5 -3-v5, a, (©) z (d) 5, The principal value of tan 1),, Fl is:, 27., t a, (a) a (b) é, t, = d), © 5 (d) x 28, ey -2 |, The principal value of sec" | “=, 5 2, a b) =, ® 3 Dy 29., (c) 3 (d) None of these, The inverse of cosine function is defined in the, intervals :, -1, (a) [-7,0] (b) ae, 30., , ea] a, , If sin’! x= y, then:, , , , , , . The value of tan~? (tan 32) cos: 5 (cos ue) is:, n, a) 0 b) =, (a) (b) 3, 1 20, me ay 2, iC) 6 (d) 3, The domain of the function cos“! (2x -1) is:, INCERT Exemplar], (a) [0,1] () E44), () 1,1) (d) [0,7], , . The domain of the function defined by f(x) = sin”!, De INCERT Exemplar], (a) [1,2 () E11), , (©) [0,1] (d) none of these, The value of cos“! (cos 2) is equal to:, INCERT Exemplar], 1 3m, a By 2, {a) 3 (b) 3, Sn 7%, Be ay, (c) 2 (d) 2, . Solve sin (tan-!x), | x1 <1is equal to: [NCERT], 1, (a) (b), 1 a x, © Faw O Tee, , , , , , Choose the correct option :, , (a) Both (A) and (R) are true and R is the correct, explanation A., , (b) Both (A) and (R) are true but R is not correct, , explanation of A., , (c) Ais true but R is false., , (d) Ais false but R is true., , , , , , -T 7, (a) O<y<x (b) a Ass, (©) O<y<n (d) Fed, sin (z -sin- (- )) is equal to:, 3 2 a ‘, (a) 1/2 (b) 1/3, (© 1/4 (d) 1 31., The value of, “1 1 ca [© ~le n)). ae, tan Be +cot a +tan sin| — z is:, T Tt, (a) S (b) DD, () -= (dy =, a 1, The value of tan=! [2 sin (2 cos“ 4)| is: 33., T 2n, (a) 3 (b) 3, o= @ =, , Assertion (A): sin | (sin 3) =3, Reason (R) : For principal values sin“ (sin x) = +x, Assertion (A) : The solution of system of equations, , 2, cos! x+ (sin! y)? = ae, , 4 2, and (cos! x) (sin! y)? = e is x= cos and y=+1,, , Vpel, Reason (R) : AM = GM., , 2u, Assertion (A): If sin x; = nnnweN, i, , a “, Pape, a te, , ee, oe, , n, Then, & %j)=, i=l 1, , i i, , Reason (R) :- é <sintx< 2 Vxef-L1], —_—_—___4_—

Page 3 : 34. Assertion : The equation 2(sin-! x)? - 5(sin- | x + 2), =0., , Reason: sin | (sin x) = x if x € [- 1.57, 1.57]., , 35. Two men on either side of temple of 30m height, observe ils top at the angle of elevation « and [3, respectively. The distance between the two men, is 403 m and distance between men A and the, , temple is 303 m., , , , , de, , Based on above information answer the following, questions:, (i) Find ZCAB=a=, , 40/37, , , , (ii) ZCAB=a.=?, , (a) cost = (b) cost, , (©) eos 1B (d) cos-! 3, (ii) 2BCA = B=?, , (a) tant (b) tan !2, , (9 tan 4 (a) tant V3, (iv) ZABC =?, , @ = w =, , @ 4 @ =, , (v) Domain and range of cos ! x?, , , , , , , , , , , , , , , , , , rte 24. 2 (a) 1,1), On) (b) [-1,1], 0, =), @ sint} &) sint in, z : © GEL @ ¢10,|-2,5, 3 22, (c) sin rs (d) sin t2, Solutions, 2 2m, 1 = 4. oe, (b) 5 @ >, Explanation : Explanation :, Weihave, cos“ [eos (- 680°)] = cos [cos (720° - 40°)], cos [se Be cos"! | =0 = cos" [cos (—40°)], ° = cos [cos (40°)], { + 2 ly = es, > sin Eros x =cos '0 =40°= 20, > sin? 2p coert ve ® af, 5 2 5. (d), = sind Zao 2 2, au 5 epee a Explanation :, 4 mn 442 Let sin! x= 0,, = SoS ea then sinO =x, 1 12 = cosec 8 = A, = 5 x, > cosec? 0 =, 2 => L+cot? 0, gee, 5, ir 1-3?, ae > cot @=, 2. (a) [- Pal =, ( ao x, 3. (b) [0-2] - {3} => cot (sin! x) =, ; ) 5