Question

sin square x + 4 sin x + 5 lies in​

Answer 1

Answer:

Let

$y = \sin(x)$

Your equation becomes

${y}^{2} + 4y + 5 \\ where \: \: - 1 \leqslant y \leqslant 1$

So now take derivative

$2y + 4 = 0 \\ y = - 2$

So equation attains it's maxima at -2 , so in [ -1 , 1 ]

function is monotonic increasing

$y = - 1 \implies { - 1}^{2} - 4 + 5 = 0 \\ \\ y = 1 \implies1 + 4 + 5 = 10$

So function lies in [ 0 , 10 ]