Question

Find the range of

$f\left(x\right)=\sin x+\cos x+3$, Range is [a,b]. find ab?

Answer 1

We know, $-\sqrt{a^2+b^2}\le a\sin x+b\cos x\le \sqrt{a^2+b^2}$
Hence range of function $f\left(x\right)=\sin x+\cos x+3$
is, $[-\sqrt{2}+3,\sqrt{2}+3]$
Hence $ab=3^2-2=7$