Question

cosecA-2cot2AcosA=2sinA. plz prove it

Answer 1

Given:

$\sf \: cosecAcosecA-2cot2AcosA=2sinA$

To Find:

• To Prove it

step by step explanation

$\sf \: = \frac{1}{sinA} - 2 \frac{cos2A}{sin2A} .cosA \\ \\ = \sf \: \frac{sin2A - 2sinA.cosA.cos2A}{sin2A.sin2A} \\ \\ \sf \: = \frac{sin2A - cos2A.sin2A}{sin2A.sinA} \\ \\ \sf \: = \frac{ sin2A (1 - cos2A)}{sin2A.sinA} \\ \\ \sf \: = \frac{1 - 2 {sin}^{2} A + 1}{sinA} \\ \\ \sf \: = \frac{2 {sin}^{2}A }{sinA} = 2 \: sinA$