Question

prove that cotA -cosA/cotA+cosA=cosecA-1/cosecA+1​

Answer 1

Answer:

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Answer 2

❥${\red{\underline{\underline{\huge{\mathtt{Solution:-}}}}}}$

$\frac{cotA-cosA}{cotA+cosA}$

★We know cotA=$\frac{cosA}{sinA}$

→$\frac{\frac{cosA}{sinA}-cosA}{\frac{cosA}{sinA}+cosA}$

→$\frac{\frac{cosA(1-sinA)}{sinA}}{\frac{cosA(1+sinA)}{sinA}}$

→$\frac{cosA(1-sinA)}{sinA}×\frac{sinA}{cosA(1+sinA)}$

→$\frac{1-sinA}{1+sinA}$

★We know sinA= $\frac{1}{cosecA}$

→$\frac{1-\frac{1}{cosecA}}{1+\frac{1}{cosecA}}$

→$\frac{\frac{cosecA-1}{cosecA}}{\frac{cosecA+1}{cosecA}}$

→$\frac{cosecA-1}{cosecA}×\frac{cosecA}{cosecA-1}$

→${\green{\large{\bold{\frac{cosecA-1}{cosecA+1}}}}}$

Hence proved______!!