Question

F(x) = (sinx + cosx)^2, find the minimum value of F(x)
(B) 1
(A) O
(C) 2
(D) 3

Answer 1

Step-by-step explanation:

We have,

$f(x) = (\sin(x) + \cos(x) ) ^{2}$

$\implies \: f(x) = \sin^{2} (x) + \cos^{2} (x) + 2 \sin(x) \cos(x)$

$\implies \: f(x) = 1 + 2 \sin(x) \cos(x)$

$\implies \: f(x) = 1 + \sin(2x)$

We know,

$- 1\leqslant \sin(2x) \leqslant 1$

$\implies 0\leqslant1 + \sin(2x) \leqslant 2$

So,

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

So, minimum value of f(x) is 0