Question

What is the smallest possible value of $x$ (in degrees) for which $\cos x-\sin x=\frac{1}{\sqrt{2}}$?

• A. $5^o$
• B. ${12}^o$
• C. ${15}^o$
• D. ${18}^o$
• E. ${30}^o$

Answer 1

Answer: (C)

${15}^o$

Given $\cos x-\sin x=\frac{1}{\sqrt{2}}$
By squaring on both sides, we get

$1-\sin 2x=\frac{1}{2}$
$\Rightarrow \sin 2x=\frac{1}{2}$

$\Rightarrow 2x=30$ and $x=15$ (smallest possible value)