Page 1 :
Term-!, CHAPTER, , , , INTRODUCTION TO, TRIGONOMETRY &, , , , TRIGONOMETRIC IDENTITIES, , Syllabus, 5 Sa, , (GM Elr asa), , , , ID ©. 1. The value of the expression (cosec (75° + 0) 2-3: The value of (tan 1° tan 2° tan 3°... tan 89°) is:, , ~ sec (15° — 0) - tan (35° + 0) + cot (35° 6)] is: (A) 0 (B) 1, (A) -1 B) 0, , Oe ©2 w+ u, © 1 5 f z, , Ans. Option (B) is correct. aed eeie, Explanation: cosec (75° + 8) ~ sec (15° - 8) — tan, , (55° + 8) + cot (35°-0) i, , = cosec| 90° — (15° —8)]—sec(15°— 6), , ~tan(55° 5°, , = sec(I5°-0)~s, , , , , , =0 (i, Q.2. If cos (a + fi) = 0, then sin (a - f) can be reduced to, (A) cos p (B) cos 26,, (C) sina (D) sin 2a IR, , , , , , Ans. Option (B) is correct.

Page 4 :
sy, AN, , , , , , , , , , , , , , , , Direc Inthe following questions, A statement, of Assertion (A) is followed by a statement of, Reason (R). Mark the correct choice as, , , , (A) Both Aand Rare true and Ris the correct explanation, of A, , (B) Both A and R are true but R is NOT the correct, explanation of A, (C) Ais true but R is false, (D) Ais false and Ris True, Q. 1, Assertion (A): Cot A is the product of Cot and A., Reason (R): The value of sinO increases as 0, increases., , Ans. Option (D) is correct., , Explanation: In case of assertion:, , cot A is not the product of cot and A. It is the, cotangent of ZA., , ©. Assertion is incorrect., , In case of reason:, , The value of sin @ increases as @ increases in, interval of 0°< 6° < 90°, , ~. Reason is correct:, , Hence, assertion is incorrect but reason is, correct., , Q.2. Assertion (A); The value of @P47° j., cotag®, , Reason (R): The value of the expression (sin 80° —, cos 80°) is negative., Ans. Option (C) is correct,, , Explanation: In case of assertion:, tan47°, we, cot 43°, , tan47°, cot (90° = 47°), ~ tan47°, tand7>, “. Assertion is correct,, In case of reason:, 80° is near to 90°, sin 90° = 1 and cos 90° = (), So, the given expression sin 80° - cos 80° > 0, , So, the value of the given expression is positive., * Reason is incorrect:, , assertion is correct but reason. is, , incorrect., Q.3. Assertion (A): If tan A, (A + B) is 90, , Reason (R): If sec 0 sin Q = 0, then the, , , , cot B, then the value of, , value of 0 is, , (B) is correct., , Explanation: In case of assertion:, , tan A = cot B (Given) |, > tan A = tan(90°~ B) |, [= tan (90° = 0) = cot 9] |, PA A =90°-B, Hence, A+B = 90°,, , .”. Assertion is correct,, In case of reason:, Given, sec O.sin0d = 0, , , , 8, =0, ae cos @, or, tan@ = 0 = tan 0°, By 0=0, «, Reason is correct:, , Hence, both assertion and reason are correct, but reason is not the correct explanation for, assertion., , Q.4. Assertion (A): If x = 2 sin? 6 and y = 2 cos? 6 + |, , then the value of x + y = 3., 5, Reason (R): If tan a = Ty’ then the value of sec ais, , 13, 12, , Ans. Option (B) is correct., , Explanation: In case of assertion:, , , , , , We have x =2sin?6, and ¥ =2cos*6+1, Then, x+y =2sin?0 + 2cos?0 +1, = Asin?0 + cos* 0) + 1, 2x1+1, [-" sin? 0 + cos? = 1], =2+1=3,, . Assertion is correct., In case of reason:, tana = a, 12, , Unsing identity; sec a ~ tan? a = 1, seca =1+ tan?a, , = seca = (5), , 25, = 1+, arr |, |

Page 5 :
INTRODUCTION TO TRIGONOMETRY AND TRIGONOMETRIC IDENTITIES, , Q.5. Assertion (A): Ifk + 1 = sec’ 6 (1 + sin 8) (1—sin 0),, then the value of kis 1., Reason (R): If sin @ + cos @ = V3 then the value of, tan 0 + cot Ois 1., , ‘Ans. Option (D) is correct., , Explanation: In case of assertion:, k +1 = sec? 0(1 + sin 6)(1 —sin 0), J or k +1 = sec*@(1—sin?6), or, k +1 [email protected]?@, [~ sin? + cos? 0 = 1), , 1, or, k+1 =sec*0 x ae, or, k+1=1, or, k=1-1, eo k=0., ~, Assertion is incorrect., , In case of reason:, Given sin@ + cos® = V3, , Squaring on both sides,, (sin 8 + cos 6)> = (V3)?, sin?@ + cos?@ + 2 sin @.cos® =3, , , , , , , , 1+2sin0@cos@ =3, 2sin@cos0 =2, sin @ cos 8 = 1 w= (i), sin® _ cos®, tan@ + cot® = ——+——, cos@ sin®, _ sin?2@+cos"0, cos@sin®, i, ~ cos@sin®, eT, 1, , [From equation (i)], .. Reason is correct:, , Hence, Assertion is incorrect but reason is, correct., , PINAY oer, , Attempt any four sub-parts from each question., Each sub-part carries 1 mark., , I. Read the following text and answer the following, question on the basis of the same:, , , , , , 'Skysails’ is that genre of engineering science that, uses extensive utilization of wind energy to move, a vessel in the sea water. The sky sails technology, , Q.6. Assertion (A): If sin A =, , Bigs, , , then the value of, , 2 -1, 2cotA-1lis —., , Reason (R): If 8 be an acute angle and 5 cosec 0 = 7,, then the value of sin 9 + cos* 6-1 is 10., Ans. Option (C) is correct., Explanation: In case of assertion:, %ot2A-1 = 2(cosec* A-1)-1, cot? @ =~ 1 + cosec* 0), , , , , , , , sin? A, =—-3, (¢, dco A-1 = §, 3, .. Assertion is correct., In case of reason:, Given, 5cosec® =7, cosec 8 = L,, or, 5, 5, in@ = =, or, sin 7, , 1, [- cosec 0 = ane!, , sin 0 + cos?@-1 = sin @- (1 -cos* 6), = sin @-sin? 6, , , , ea ee, 49 49, -. Reason is incorrect:, Hence, assertion is correct but reason is, incorrect., , allows the towing kite to gain a height of anything, between 100 m to 300 m. The sailing kite is made, in such a way that it can be raised to its proper, elevation and then brought back with the help of, a telescopic mast that enables the kite to be raised, properly and effectively.