JEE Main20204 Sep 2020Evening ShiftMathematicsFunctionsActual

The minimum value of 2 sin x + 2 cos x is :

Options

A2 - 1 + 1 2
B2 - 1 + 2
C2 1 - 2
D2 1 - 1 2

Correct answer

D. 2 1 - 1 2

Step-by-step solution

Using A . M ≥ G . M . 2 sinx + 2 cosx 2 ≥ 2 sinx · 2 cosx ⇒ 2 sinx + 2 cosx ≥ 2 1 + sinx + cosx 2 Now - 2 ≤ sinx + cosx ≤ 2 So minimum value of 2 sinx + 2 cosx = 2 1 + - 2 2 = 2 1 - 1 2

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