Question

Prove: [(tan^2theta+1)(cos^2theta-1)]=1-sec^2theta

Answer 1

tan^2 = sin^2/cos^2 = s^2/c^2

(s^2/c^2+1)(c^2-1) = s^2 -s^2/c^2 +c^2 -1
but s^2 + c^2 = 1
so we have
-s^2/c^2
= -(1 - c^2)/c^2
= - 1/c^2 + 1
= 1 - sec^2