How to verify this identity, with steps

Question

cos^2x/tanxsinx+tanx=(1-sinx)/tanx

Answer 1

Working on the left side only.

In the numerator replace cos²(x) with (1-sin²x),

In the denominator factor out tan(x) to give tan(x)(sinx+1)

Now factor the numerator as a difference of squares (1-sinx)(1+sinx)

Rearrange the terms in the 2nd factor of the denominator (1+sinx)

Now the (1+sinx) factor in the numerator and denominator cancel out., leaving (1-sinx)/tan(x)

Q.E.D.

Answer 2

Cos²x/( tanx sinx + tanx)

(1-sin²x)/ (sin²x/cosx +sinx/cosx)

(1-sin²x)/(sin²x+sinx)/cosx

factor numerator and denominator

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

l+sinx cancels out

(1-sinx)/ (sinx/cosx)

(1-sinx)/ tanx