Question

verify the identity 1+sin(x)=(cos^(2)(x))/(1-sin(x))

Answer 1

\(\cos^2x+\sin^2x=1\)
\(\cos^2x=1-\sin^2x\)
\(1-\sin^2x=1^2-\sin^2x\)
\(=(1-\sin x)(1+\sin x)\)
consider the trigonometric expression on the right side of the equation. then replace the \(\cos^2x\) with \((1-\sin x)(1+\sin x)\)
then cancel any common factors. if the remaining part after simplification is equal to \((1+\sin x)\) then the equation is valid. does that help?

Answer 2

@jsaavedr