Question

Find the
range of
y =
2 sin^2x + 3 cos(2x+7)​

Answer 1

Step-by-step explanation:

We have,

$y = 2 \sin^{2} (x) + 3 \cos(2x + 7)$

Now,

$0\leqslant \sin^{2} (x) \leqslant 1$

$\implies \: 0\leqslant 2\sin^{2} (x) \leqslant 2$

And,

$- 1\leqslant \cos(2x + 7) \leqslant 1$

$\implies - 3\leqslant 3\cos(2x + 7) \leqslant 3$

So, range of f(x) will be,

$[0 , 2] \: \cap \: [ - 3 , 3]$

$f(x) \in[0 , 2]$