Establish the identity of sin θ(cot θ + tan θ) = sec θ

Question

Write the left side in terms of sine and cosine.

sin θ(_______________).

Can someone please help? Thank you!

Answer 1

sinx(cotx+tanx) = secx

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

sin(cosx/sinx) + sinx(sinx/cosx) = 1/cosx

cosx +sin^2x/cosx = 1/cosx

cos^2x/cosx + sin^2x/cosx= 1/cosx

(cos^2x + sin^2x)/cosx= 1/cosx

1/cosx = 1/cosx

cos^2x + sin^2x= 1