Question #2491

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

Expert's answer

Due to the identity

cos^{2}x+sin^{2}x=1

the numerator is equal to sin^{2}x

In the denominator we open brackets by standard formula:

(1-sinx) (1+sinx)=1-sin^{2}(x)

which gives cos^{2}(x)

Hence we get

sin^{2}x/ cos^{2}x = tan^{2}x

cos

the numerator is equal to sin

In the denominator we open brackets by standard formula:

(1-sinx) (1+sinx)=1-sin

which gives cos

Hence we get

sin

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