cosec A - 2cot 2A cos A = Options: A . &nbsp 2sinA B . &nbsp secA C . &nbsp 2cosAcotA D . &nbsp None of these

Answer: Option A : A cosec A - 2 cot 2A cos A = 1 s i n A - 2 c o s A c o s 2 A s i n 2 A = 1 s i n A - 2 c o s A c o s 2 A 2 s i n A c o s A = 1 − c o s 2 A s i n A = 2 s i n 2 A s i n A = 2sin A.

cosec A - 2cot 2A cos A =

Question

cosec A - 2cot 2A cos A =

Options:

A . 2sinA

B . secA

C . 2cosAcotA

D . None of these

Answer: Option A
:
A

cosec A - 2 cot 2A cos A =
$\frac{1}{s i n A}$ -
$\frac{2 c o s A c o s 2 A}{s i n 2 A}$

=
$\frac{1}{s i n A}$ -
$\frac{2 c o s A c o s 2 A}{2 s i n A c o s A}$ =
$\frac{1 - c o s 2 A}{s i n A}$ =
$\frac{2 s i n^{2} A}{s i n A}$

= 2sin A.

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