Exams › SSC CGL (Prelims) › General

If $\sin x + \cos x = \sqrt{1.5}$, what is the value of $\sin x - \cos x$?

1. 1 / $\sqrt{2}$
2. 1
3. 1/2
4. $\sqrt{2}$

Correct answer: 1 / $\sqrt{2}$

Solution

Given $\sin x + \cos x = \sqrt{1.5}$, squaring gives $1 + 2\sin x\cos x = 1.5$, so $\sin x\cos x = 0.25$. Then $(\sin x - \cos x)^2 = 1 - 2\sin x\cos x = 1 - 0.5 = 0.5$, so $\sin x - \cos x = \pm \frac{1}{\sqrt{2}}$. The matching option is $\frac{1}{\sqrt{2}}$.

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