Question

Solve for x
$sin \: x \: + \: cos \: x \: \leqslant \frac{1}{sin \: x}$
please solve its urgent.

Best answer would be marked as brainliest.

Answer 1

We know that

$- \sqrt{2} \leqslant \sin( \alpha ) + \cos( \alpha ) \leqslant \sqrt{2}$

But according to question,
$\frac{1}{ \sin( \alpha ) } \leqslant \sin( \alpha ) + \cos( \alpha )$
Therefore,
$\frac{1}{ \sin( \alpha ) } \leqslant \sqrt{2} \\ \csc( \alpha ) \leqslant \sqrt{2}$
Now draw graph of csc(x) to get the answer.
Hope this helps