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Question

If the function f(x)=λ|sinx|+λ2|cosx|+g(λ),λR, where g is a function of λ, is periodic with fundamental period π2, then

A
λ=0,1
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B
λ=1
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C
λ=0
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D
λ=1
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Solution

The correct option is B λ=1
Given f(x) is periodic with fundamental period π2.
So, f(π2+x)=f(x) xR
λ|cosx|+λ2|sinx|+g(λ)=λ|sinx|+λ2|cosx|+g(λ)
(λλ2)|cosx|+(λ2λ)|sinx|=0 xR
λλ2=0λ=0,1
But λ=0 is rejected as if λ=0, then f(x) becomes a constant function.
Hence, λ=1

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