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Question: Let f(x) = Maximum {sinx, cosx} ∀ x ∈ R. Minimum value of f(x) is...

Let f(x) = Maximum {sinx, cosx} ∀ x ∈ R. Minimum value of f(x) is

A

(1 – 2\sqrt { 2 })

B

-1

C

(1−12)\left( 1 - \frac { 1 } { \sqrt { 2 } } \right)

D

12\frac { 1 } { \sqrt { 2 } }

Answer

12\frac { 1 } { \sqrt { 2 } }

Explanation

Solution

Bold line represents the graph of f(x) in [0, 2π] clearly minimum value of f(x) is −12- \frac { 1 } { \sqrt { 2 } }