CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that y=4sinθ2+cosθθ is an increasing function in [0,π2].

Open in App
Solution

Let f(θ)=4sinθ2+cosθθ, θ[0,π2]
Now f(θ)=4(1+2cosθ)(2+cosθ)21
The function is continuous in [0,π2] and differentiable in (0,π2).
Then from Lagrange's Mean Value Theorem we get, there exist c(0,π2) such that,
f(π2)f(0)π2=f(c)>0
So we have f(θ)>0,θ(0,π2).
Now f(0)=13 and f(π2)=0.
So, f(θ)0θ[0,π2].
This gives the function f(θ) is monotone increasing in [0,π2].
So y is an increasing function in that interval.

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