Question

Prove that:cot A - cos A / cot A + cos A = cosec A - 1 / cosec A + 1

Answer 1

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Answer 2

Answer:

$\frac{cotA - cosA}{cotA+cosA}=\frac{cosecA-1}{cosecA+1}$

Step-by-step explanation:

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

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

$We\:know \:that \\\boxed {cotA= \frac{cosA}{sinA}}$

$=\frac{cosA\left(\frac{1}{sinA}-1\right)}{cosA\left(\frac{1}{sinA}+1\right)}$

$=\frac{\left(\frac{1}{sinA}-1\right)}{\left(\frac{1}{sinA}+1\right)}$

$= \frac{cosecA-1}{cosecA+1}\\=RHS$

Therefore,

$\frac{cotA - cosA}{cotA+cosA}=\frac{cosecA-1}{cosecA+1}$

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