Question

cosecA + 2cosec2A = secA.cotA/2​

Answer 1

there is nothing special, you just need to apply transformation formula.Here , I have uploaded the pic of solution.

I HOPE IT WILL HELP YOU.

Answer 2

$cosec\ A + 2cosec\ 2A = sec\ A\ cot \frac{A}{2}$

Solution:

Given that, we have to prove:

$cosec\ A + 2cosec\ 2A = sec\ A\ cot \frac{A}{2}$

Take the LHS

$cosec\ A + 2cosec\ 2A \\\\We\ know\ that\ sin\ x = \frac{1}{cosec\ x}\\\\Therefore\\\\\frac{1}{sin\ A} + \frac{2}{sin\ 2A} \\\\We\ know\ that\ sin2A = 2sinAcosA\\\\\Therefore$

$\frac{1}{sinA} + \frac{2}{2sinAcosA}\\\\\frac{1}{sinA} + \frac{1}{sinAcosA}\\\\\frac{cosA + 1}{sinAcosA}\\\\We\ know\ that\ 1 + cosA = 2cos^2\frac{A}{2}\\\\Therefore\\\\\frac{2cos^2\frac{A}{2}}{sinAcosA}\\\\We\ know\ that\ sinA = 2sin\frac{A}{2}cos\frac{A}{2}\\\\\frac{2cos^2\frac{A}{2}}{ 2sin\frac{A}{2}cos\frac{A}{2} cosA}\\\\\\\frac{cos\frac{A}{2}}{sin \frac{A}{2}cosA}\\\\\\\frac{1}{cos A} \times \frac{cos \frac{A}{2}}{sin \frac{A}{2}}\\\\sec\ A cot \frac{A}{2}$

Thus, LHS = RHS

Thus proved

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(Cot A-1)2+(cot A+1)2=2cosec2a

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Prove tanA+ cotA = 2cosec2a

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