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

Prove that: |cos θ cos (60θ) cos (60+θ)|14 for all values of θ

Open in App
Solution

|cos θ cos (60θ) cos (60+θ)|=|cos θ(cos2 60sin2 θ)|{since cos(AB) cos (A+B)=cos2Asin2 B}=cos θ(14sin2θ)=cos θ 14(14 sin2θ)=14 cos θ (14(1cos2 θ))=14 cos θ (3+4 cos2 θ)

=14(4 cos 3θ3 cos θ)=14 cos 3θ 14 {since |cos 3 θ|1}

So,

|cos θ cos (60θ) cos (60+θ)|14


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