Answer to Question #2491 in Trigonometry for jenny

Question

What steps would you take to verify this? Thank you!!! :)
(1-cos^2(x)) / ((1-sinx) (1+sinx)) = tan^2(x)

Answer 1

Due to the identity
cos²x+sin²x=1
the numerator is equal to sin²x

In the denominator we open brackets by standard formula:
(1-sinx) (1+sinx)=1-sin²(x)
which gives cos²(x)

Hence we get
sin²x/ cos²x = tan²x