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  • Prove the following cos(3pi/4+x) - cos(3pi/4-x) = -2^(1/2)sinx

Q (11) Prove the following

\small \cos \left ( \frac{3\pi }{4}+x \right ) - \cos\left ( \frac{3\pi }{4} -x\right ) = -\sqrt{2} \sin x
 

Answers (1)

We know that 

[ cos(A+B) - cos (A-B) = -2sinAsinB ]

By using this identity 

\cos \left ( \frac {3\pi}{4}+x \right ) - \cos \left ( \frac {3\pi}{4}-x \right ) = -2\sin\frac{3\pi}{4}\sin x = -2\times \frac{1}{\sqrt{2}}\sin x\\ \\ = -\sqrt{2}\sin x                                 R.H.S.

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