Question

Prove that
CosA+sinA/CosA-SinA - CosA-sinA/CosA+SinA =2tan2A

Pleases explain step by step

Answer 1

here is your answer dude

on the first page the last step has been cut

= 4 * (cos A Sin A)÷ (cos^2A - sin^2A)

Answer 2

Given:  $\frac{\cos A +\sin A}{\cos A -\sin A}- \frac{\cos A -\sin A}{\cos A +\sin A}= 2\tan 2A$

Explanation:

$\frac{\cos A +\sin A}{\cos A -\sin A}- \frac{\cos A -\sin A}{\cos A +\sin A}= 2\tan 2A$

$\\\\\cos 2x =\cos^2 x-\sin^2x \\\\\text{taking LCM}\\\\\frac{\cos^2A+\sin^2A+2\cosA\sinA- (\cos^2A+\sin^2A-2\cosA\sinA)}{\cos 2 A}\\\\\frac{\sin 2A+\sin 2A}{\cos 2 A}\\\\\frac{2\sin 2 A}{\cos 2 A}\\\\= 2\tan2A$

hence proved

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