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Question: \[\text{cosec }A - 2\cot 2A\cos A =\]...

cosec A−2cot⁡2Acos⁡A=\text{cosec }A - 2\cot 2A\cos A =

A

2sin⁡A2\sin A

B

sec⁡A\sec A

C

2cos⁡Acot⁡A2\cos A\cot A

D

None of these

Answer

2sin⁡A2\sin A

Explanation

Solution

cosecA−2cot⁡2Acos⁡A=1sin⁡A−2cos⁡Acos⁡2Asin⁡2A\text{cosec}A - 2\cot 2A\cos A = \frac{1}{\sin A} - \frac{2\cos A\cos 2A}{\sin 2A}

=1sin⁡A−2cos⁡Acos⁡2A2sin⁡Acos⁡A=1−cos⁡2Asin⁡A=2sin⁡2Asin⁡A= \frac{1}{\sin A} - \frac{2\cos A\cos 2A}{2\sin A\cos A} = \frac{1 - \cos 2A}{\sin A} = \frac{2\sin^{2}A}{\sin A}

=2sin⁡A= 2\sin A.