Question

Buktikan identitas trigonometri
a) Tan^2X - sin^2x = tan^2X x sin^2X
b) sinX / 1 + cosX = sec X - tan X

Answer 1

A)
tan² x - sin² x = sin² x / cos² x - sin² x
= (sin² x - sin² x cos² x)/ (cos² x)
= sin² x ( 1 - cos² x) / cos ² x
= sin² x (sin²x) / cos² x)
= sin² x/cos²x . sin² x
= tan² x. sin² x

b)
sin x / (1 + cos x)   X (1 - cos x)/(1- cos x)=
= sin x (1 - cos x) / (1 - cos² x)
= sin x (1 - cos x) / (sin² x)
= (1 - cos x)/ (sin x)
= 1/sin x  - cos x/sin x
= csc x - cot x