If sin cos then what is sin minus cos equal to ........

Quantitative Aptitude (CDS) Trignometry

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If sin $\Theta$ cos $\Theta$ = $\frac{\sqrt{7}}{2}$ = , then what is sin $\Theta$ − cos $\Theta$ equal to?

1/2

$\sqrt{2}$

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Explanation:

As,sin sin $\Theta$ +cos cos $\Theta$ = √7/2
Let sin sin $\Theta$ −cos cos $\Theta$ =a
As we know that
(x + y)² + (x − y)² = 2(x² + y²)
Then,
(sin sin $\Theta$ +cos cos $\Theta$ )² + (sin sin $\Theta$ −cos cos $\Theta$ )² = 2( $\Theta$ + $\Theta$ )²
=>(√7/2)²+ a² = 2 × 1
=>a²=2-7/4
a=1/2
Hence sin sin $\Theta$ −cos cos $\Theta$ =1/2