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

If A+B+C=π, then prove that sin2A+sin2B+sin2C=4sinAsinBsinC

Open in App
Solution

Consider the problem

A+B+C=π

sin2A+sin2B+sin2C

=2sin(A+B)cos(AB)+2sinCcosC=2sin(πC)cos(AB)+2sinCcosC=2sinCcos(AB)+2sinCcosC=2sinC(cos(AB)+cos(π(A+B)))=2sinC(cos(AB)cos(A+B))=2sinC(2sinBsinA)=4sinAsinBsinC

Hence, LHS=RHS

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