Question

Cosx/(1+sinx) = (1-sinx)/cosx

Verify this identity

Thanks

Answer 1

calculate the left side:

cos x / (1+ sin x)

multiply by (1- sinx/1-sinx)

to get

cos x (1-sinx) / (1+sinx)(1-sinx)

simplify the numerator than the denominator to get

cosx - cosx sinx / 1-sin^2x

apply Pythagorean identity to get

cos x - cosx sin x / cos^2 x

which simplifies to

1-sinx/cos x which equal the right side so it is true