Question

Prove:
(cosecx-secx)/(cosexc+secx)=(1-tanx)/(1+tanx)

Answer 1

lets begin
can you change the LHS in terms of sin and cos only

Answer 2

\[\begin{align*}\frac{\csc x-\sec x}{\csc x+\sec x}&=\frac{1-\tan x}{1+tan x}\\\\
\frac{\frac{1}{\sin x}-\frac{1}{\cos x}}{\frac{1}{\sin x}+\frac{1}{\cos x}}&=\\\\
\frac{\frac{\cos x-\sin x}{\sin x\cos x}}{\frac{\cos x+\sin x}{\sin x\cos x}}&=\\\\
\frac{\cos x-\sin x}{\cos x+\sin x}&=\\\\
\frac{\cos x-\sin x}{\cos x+\sin x}\cdot\frac{\frac{1}{\cos x}}{\frac{1}{\cos x}} &=\\
\vdots&=\end{align*}\]

Answer 3

Thank you! ^_^