Question

(tanTheta+secTheta-1)/(tanTheta-secTheta+1) = (1+sinTheta)/(cosTheta)

Prove that the two expressions are equal.

Answer 1

i find it easiest to replace cosine by \(a\) and sine by \(b\) and do the algebra first that way

Answer 2

\[\frac{\frac{b}{a}+\frac{1}{a}-1}{\frac{b}{a}-\frac{1}{a}+1}\] is the left hand side.
right hand side is
\[\frac{1+b}{a}\] and there is proably precious little actual trig involved, although don't forget that since \(a\) is cosine and \(b\) is sine if you see \(a^2+b^2\) you can replace it by \(1\)