Buktikan a. (1-cos^2 x) ( 1+cot^2x) =1 b. Sin + (cst t - sin t) = cos^2 t c. 1-csc^2 t / csc^2 t = - 1 /sec^2 t Dengan identitas trigono metri Mohon bantuannya

Trigonometri

1][
(1 - cos²x)(1 + cot²x) = 1
sin²x . csc²x = 1
sin²x . 1/sin²x = 1
1 = 1
(Terbukti)

2][
sin t + (csc t - sin t) = cos²t
1/csc t + (1/sin t - sin²t/sin t) = cos²t
1/csc t + (1 - sin²t)/sin t = cos²t
sin t + (1 - sin²t)/sin t = cos²t
sin²t/sin t + (1 - sin²t)/sin t = cos²t
(sin²t + 1 - sin²t) / sin t = cos²t
1/sin²t = cos²t
cos²t = cos²t
(Terbukti)

3][
(1 - csc² t) / csc² t = - 1/sec² t
-cot² t / csc² t = -1/sec² t
-(cos t/sin t)² / (1/sin² t) = -1/sec² t
-(cos t/sin t)² . sin² t = -1/sec² t
-cos t = -1/sec² t
-1/sec²t = -1/sec² t
(Terbukti)