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

Prove the following:
sin26xsin24x=sin2x,sin10x

Open in App
Solution

LHS =sin26xsin24x

=(sin6x+sin4x)(sin6xsin4x) ... [a2b2=(a+b)(ab)]

We know that, sinA+sinB=2sin(A+B2)cos(AB2)

LHS =[2sin(6x+4x2)cos(6x4x2)][2cos(6x+4x2)sin(6x4x2)]

=[2sin(10x2)cos(2x2)][2cos(10x2)sin(2x2)]

=2sin5xcosx×2cos5xsinx

=2sin5xcos5x×2sinxcosx

=sin10x×sin2x ...[sin2θ=2sinθcosθ]

= RHS

Hence proved.

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Inequalities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon