Tolong dibantu ya ....

jawab


(1)
a)  cos 2c/ (cos c- sin c) = cos c + sin c
cos 2c / (cos c - sin c) =
= (cos c + sin c)(cos c - sin c)/(cos c - sin c)
= cos c + sin c

b) cot b = csc 2B + cot 2 B
cot b = cos b/sin b }kalikan (2 cos b/2 cos b)
= (cos b)(2 cos b)/(2 sin b cos b)
= 2 cos² b/( sin 2b)
= (cos 2b + 1)/(sin 2b)
= cos 2b/sin 2b + 1/sin 2b
= cot 2b + csc 2b
= csc 2b + cot 2b

(2) tan (x/2) = (sin x)/(1+cos x)
tan (15/2) = (sin 15)/(1 + cos 15)
sin 15  = sin(45 - 30) = sin 45 cos 30 - cos 45 sin 30
sin 15 = 1/2 √2 . 1/2 √3 - 1/2 √2 . 1/2
sin 15 = 1/4(√6 - √2)

cos 15 = cos(45-30)= cos 45 cos 30 + sin 45 sin 30
cos 15 = 1/2 √2 . 1/2 √3 + 1/2 √2 . 1/2
cos 15 = 1/4(√6 + √2)

tan 7,5 = (sin 15)/(1 + cos 15)
= 1/4 (√6 - √2) / ( 1 + 1/4(√6 + √2))
= 1/4 (√6 - √2) / 1/4 ( 4+ (√6 +√2)
= (√6 - √2) / (4 + √6 + √2)