General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2
If the functi...
Question
If the function f(x)=λ|sinx|+λ2|cosx|+g(λ),λ∈R, 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 Bλ=1 Given f(x) is periodic with fundamental period π2. So, f(π2+x)=f(x)∀x∈R ⇒λ|cosx|+λ2|sinx|+g(λ)=λ|sinx|+λ2|cosx|+g(λ) ⇒(λ−λ2)|cosx|+(λ2−λ)|sinx|=0∀x∈R ⇒λ−λ2=0⇒λ=0,1 But λ=0 is rejected as if λ=0, then f(x) becomes a constant function. Hence, λ=1