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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions

If $\sin x+\cos x=a$,then $|\sin x-\cos x|=$________

$\begin{array}{1 1}(A)\;\sqrt {2-a^2}&(B)\;a\\(C)\;\sqrt 2&(D)\;-a\end{array} $

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1 Answer

Given :
$\sin x+\cos x=a$
$(\sin x+\cos x)^2=a^2$
$\sin ^2x+\cos ^2x+2\sin x\cos x=a^2$
$\sin x\cos x=\large\frac{a^2-1}{2}$
$(\sin x-\cos x)^2=\sin ^2x+\cos ^2x-2\sin x\cos x$
$\Rightarrow 1-2\sin x\cos x$
$\Rightarrow \large\frac{1-3(a^2-1)}{2}$
$\Rightarrow 1-a^2+1=2-a^2$
$\sin x-\cos x=\pm \sqrt{2-a^2}$
$\therefore |\sin x-\cos x|=\sqrt{2-a^2}$
Hence (A) is the correct answer.
answered Apr 22, 2014 by sreemathi.v
 

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