{rm{cosec }}A - 2cot 2Acos A =

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3.Trigonometrical Ratios, Functions and Identities

easy

${\rm{cosec }}A - 2\cot 2A\cos A = $

A

$2\sin A$

B

$\sec A$

C

$2\cos A\cot A$

D

None of these

Solution

(a) ${\rm{cosec}}\,A – 2\cot 2A\cos A $

$= \frac{1}{{\sin A}} – \frac{{2\cos A\cos 2A}}{{\sin 2A}}$

$ = \frac{1}{{\sin A}} – \frac{{2\cos A\cos 2A}}{{2\sin A\cos A}} $

$= \frac{{1 – \cos 2A}}{{\sin A}} $

$= \frac{{2{{\sin }^2}A}}{{\sin A}}$

$ = 2\sin A$.

Standard 11

Mathematics

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