Question

prove that: sinA/1+cosA=cosecA-cotA

Answer 1

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Answer 2

Answer and Explanation:

To prove : $\frac{\sin A}{1+\cos A}=\csc A-\cot A$

Proof :

Taking LHS,

$\frac{\sin A}{1+\cos A}$

Rationalize,

$=\frac{\sin A}{1+\cos A}\times \frac{1-\cos A}{1-\cos A}$

$=\frac{\sin A(1-\cos A)}{(1+\cos A)(1-\cos A)}$

$=\frac{\sin A(1-\cos A)}{1^2-\cos^2 A}$

$=\frac{\sin A(1-\cos A)}{\sin^2 A}$

$=\frac{1-\cos A}{\sin A}$

$=\frac{1}{\sin A}-\frac{\cos A}{\sin A}$

$=\csc A-\tan A$

= RHS

So, LHS=RHS hence proved.