wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

How many values of θϵ[0,π2], satisfy the relation cos θ+cos3θ+cos5θ+cos7θ=0 ?


___

Open in App
Solution

When we see such expressions, we try to use the transformation formula to simplify them. We will

combine the terms such that we will get common terms.

[(cosθ+cos3θ)+(cos5θ+cos7θ) is also fine]
2cos4θcos3θ+2cosθcos4θ=θ

cos4θ(cosθ+cos3θ)=0

cos4θ2cosθcos2θ=0

cosθcos2θcos4θ=0

cosθ=0orcos2θ=0 or cos4θ=0

We want only those values of θϵ[0,π2]
θ=π2or2θ=π2or4θ=π2or3π2
θ=π2orθ=π4orθ=π8orθ=3π8
4 values


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