If \cot A = [{\sin B }/ (1 - \cos B)], thenwhat is the value of \cot 2 A ?

SSC CGL Model Paper 18

Question : 71 of 100

Marks: +1, -0

\cot A = [{\sin B }/ (1 - \cos B)]

, thenwhat is the value of

\cot 2 A

Solution:

\cot A = {\sin B }/ {1 - \cos B}

∴

\cot 2 A={\cot2 A - 1} /{2 \cot A}

={({\sin B }/ {1 - \cos B} )^2-1}/{2×{\sin B }/ {1 - \cos B} }

{({\sin B })^2-(1-\cosB)^2}/(1 - \cos B)^2

×(1 - \cos B)/{2 \sinB}

={\sin^2 B - 1 - \cos^2 B + 2 \cos B}/{2 \sin B (1 - \cos B)}

={1 - \cos^2 B - 1 - \cos^2 B + 2 \cos B}/{2 \sin B (1 - \cos B) }

={2 \cos B -2 \cos ^2 B}/{2 \sin B (1 - \cos B) }

={2 \cos B (1 - \cos B) }/{2 \sin B (1 - \cos B) }

={\cos B}/{ \sin B}=\cot B

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