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

Prove that:
cos3 2x+3 cos 2x=4cos6 x-sin6x

Open in App
Solution

RHS=4cos6x-sin6x =4cos2x3-sin2x3

Using the identity a3-b3=a-ba2+ab+b2, we get

=4cos2x-sin2x cos4x+sin4x+sin2xcos2x =4cos2x-sin2x cos4x+sin4x+sin2xcos2x

=4cos2xcos2x-sin2x2+2sin2xcos2x+sin2xcos2x =4cos2xcos22x+3sin2xcos2x =4cos2xcos22x+31-cos2x21+cos2x2
=4cos2xcos22x+341-cos22x =cos2x4cos22x+31-cos22x =cos2x4cos22x+3-3cos22x =cos2xcos22x+3 =cos32x+3cos2x=LHSHence proved.

flag
Suggest Corrections
thumbs-up
12
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Property 6
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon