Cos2A+tanA = cosec2A Prove It ??

Question

2574 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-20T14:51:40

$cos e c 2 A$ $cosec2A$ .

Sorry Question is $cot 2 A + tan A$ $cot2A+tanA$

$cot 2 A + tan A$ $cot2A+tanA$ ,

$= \frac{cos 2 A}{sin 2 A} + \frac{sin A}{cos A}$ $=(cos2A)/(sin2A)+sinA/cosA$ ,

$= \frac{cos 2 A cos A + sin 2 A sin A}{sin 2 A cos A}$ $=(cos2AcosA + sin2A sinA)/(sin2AcosA)$ ,

$= \frac{cos (2 A - A)}{sin 2 A cos A}$ $=(cos(2A-A))/(sin2AcosA)$ ,

We know that, $cos 2 A cos A + sin 2 A sin A = cos (2 A - A)$ $cos2A cosA + sin2A sinA = cos(2A-A)$ .

$:. cot2A+tanA=cosA/(sin2AcosA)$ ,

$=1/(sin2A)$ ,

$=cosec2A$ .

Proved....