Math, asked by rudradev93, 1 year ago

Find value of cot2 - 1/sin2

shivam8544: We have to find he value of

→Cot 2 a - \frac{1}{Sin 2a}Sin2a1

→\frac{Cos 2a}{Sin 2a}Sin2aCos2a - \frac{1}{Sin 2a}Sin2a1

You must keep in mind,

Cos 2 a = 2 Cos²a -1=1 -2 sin²a, Sin 2 a = 2 Sin a × Cos a

→\frac{Cos 2 a - 1}{Sin 2a}=\frac{-2 Cos^{2} a}{2 Sina\times Cosa}=\frac{-Cos a\times Cos a}{Sin a\times Cosa} = \frac{-Cos a}{Sina}= -Cot aSin2aCos2a−1=2Sina×Cosa−2Cos2a=Sina×Cosa−Cosa×Cosa=Sina−Cosa=−Cota

→ So the value of , cot2a - \frac{1}{sin2a }sin2a1 = - Cot a

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Answered by manishchaudhary

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Answered by Shardul27

$\: \: \: \: { \cot }^{2} - \frac{1}{ { \sin }^{2} } \\ = \frac{ { \cos }^{2} }{ { \sin }^{2} } - \frac{1}{ { \sin }^{2} } \\ = \frac{ { \cos}^{2} - 1 }{(1 - { \cos }^{2} )} \\ = \frac{ - ({ - \cos}^{2} + 1) }{(1 - { \cos }^{2}) } \\ = ( - 1).$

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