Question

Is (1+sin beta)/(cos beta) equivalent to (cos^2 beta)/(cos beta- cos beta sin beta)

Answer 1

To answer your question, yes, they are equivalent, since

$\dfrac{\cos^2\theta}{\cos\theta-\cos\theta\sin\theta}=\dfrac{1-\sin^2\theta}{\cos\theta(1-\sin\theta)}=\dfrac{(1-\sin\theta)(1+\sin\theta)}{\cos\theta(1-\sin\theta)}=\dfrac{1+\sin\theta}{\cos\theta}$

Similar manipulations and simplifications will show that A, B, and D are all equivalent to the starting expression, so the answer would be C.