CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
λ=1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
λ=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
λ=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
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

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Solving Trigonometric Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon