Question

Find the exact value of the following:

2. (12 pts.) Find the exact value TI a. COS -COS 24 c. sin(52.5°) sin(7.5°) b. tan 61322

Answer 1

solution al cob ( 19 )-Com use the identity A-B 2 COBA – COB = -2sin ALB. sin A- --23in (5+)-sin() 2-2 sin ( ). sinl - resin !).(-5) sin Ix x sin. 1/3 = 9+ 1 / 2 x is = { {sin (-6)= -sin 13 - 2 sin II √2 Hence i exact value

(6) Giren, tan (-1311) solution : -tan ( 42 ) identity used tan (-o) = -tono -tan (+12) .: tan(TI+)-tano - (-fans) => tan lin) tan II tant fan (1 - 1) = it tant land - 12-1 22 12+1 12-1 15.41 Hence, The exact value of tand - 13.0) - 1124 V2+1 C) sin (52-5). sin (7.8) solution : 2 sin ( 52-5), sin .s) 2 the iden Hily..609 (4-8) - (A+B) - 2 sinA.sinB :. Com 52.5-7-5) - (59.5+7-8) 0$45096 2 2 Se

- 2-12 2-12 2 (242) 11 V2 (21) V2-1 11 4. 2 . The Hence, value exact √2-1 4