Question

What is maximum value of sin x + cosx and derive it?

Answer 1

Let P = sinx + cosx
P = √2{ 1/√2 sinx + 1/√2 cosx }
= √2 { cosπ/4.sinx + sinπ/4.cosx }
[use , sin(A + B) = sinA.cosB+ cosA.sinB ]
= √2sin( π/4 + x)

we know,
-1 ≤ sin(π/4 + x) ≤ 1
multiply √2 in all sides,

-√2 ≤ √2sin( π/4 + x) ≤ √2
hence, maximum value of P = √2