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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
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The value of $\cos y\cos\big(\large\frac{\pi}{2}$$-x)$$-\cos(\large\frac{\pi}{2}$$-y\big)\cos x+\sin y\cos\big(\large\frac{\pi}{2}-x\big)$$+\cos x.\sin\big(\large\frac{\pi}{2}$$-y\big)$ is zero.If


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$\cos y\cos\big(\large\frac{\pi}{2}$$-x\big)-\cos\big(\large\frac{\pi}{2}$$-y\big)\cos x+\sin y\cos\big(\large\frac{\pi}{2}$$-x\big)+\sin y\cos\big(\large\frac{\pi}{2}-$$x\big)+\cos x\sin\big(\large\frac{\pi}{2}$$-y\big)=0$
$\Rightarrow \cos y\sin x-\cos x\sin y+\sin y\sin x+\cos x\cos y=0$
$\Rightarrow \sin(x-y)+\cos(x-y)=0$
$\Rightarrow \tan(x-y)=-1$
$\Rightarrow x=n\pi-\large\frac{\pi}{4}$$+y$
Hence (d) is the correct answer.
answered Oct 9, 2013 by sreemathi.v

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