Question

Prove (sinA-cosA)/sina + (cosA-sinA)/cosA=2-secAcscA

Answer 1

\(\large\tt \begin{align} \color{black}{\dfrac{sinA-cosA}{sinA} + \dfrac{cosA-sinA}{cosA}\\~\\
=\dfrac{sinA}{sinA}-\dfrac{cosA}{sinA} + \dfrac{cosA}{cosA}-\dfrac{sinA}{cosA}\\~\\

=1-\dfrac{cosA}{sinA} + 1-\dfrac{sinA}{cosA}\\~\\
=2-\dfrac{cosA}{sinA}-\dfrac{sinA}{cosA}\\~\\
=2-(\dfrac{cosA}{sinA}+\dfrac{sinA}{cosA})\\~\\
=2-\dfrac{cos^2A+sin^2A}{sinAcosA}\\~\\
=2-\dfrac{1}{sinAcosA}\\~\\
=2-cosecAsecA\\~\\}\end{align}\)