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Prove the identity 2csc2x=csc^2xtanz

User DolDurma
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1 Answer

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9 votes

Explanation:

Consider the LHS, after the 5th step, consider the RHS


2 \csc(2x) = \csc {}^(2) (x) \tan(x)


2 (1)/( \sin(2x) ) = \csc {}^(2) (x) \tan(x)


2 * (1)/(2 \sin(x) \cos(x) ) = \csc {}^(2) (x) \tan(x)


(1)/( \sin(x) \cos(x) ) = \csc {}^(2) (x) \tan(x)


\csc(x) \sec(x) = \csc {}^(2) (x) \tan(x)

Consider the RHS


\csc(x) \sec(x) =( 1 + \cot {}^(2) (x) ( \tan(x))


\csc(x) \sec(x) = \tan(x) + \cot(x)


\csc(x) \sec(x) = ( \sin(x) )/( \cos(x) ) + ( \cos(x) )/( \sin(x) )


\csc(x) \sec(x) = (1)/( \sin(x) \cos(x) )


\csc(x) \sec(x) = \csc(x) \sec(x)

User Lojith Vinsuka
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