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

Prove: sin(AB)sinAsinB+sin(BC)sinBsinC+sin(CA)sinCsinA=0

Open in App
Solution

Given: sin(AB)sinAsinB+sin(BC)sinBsinC+sin(CA)sinCsinA=0

LHS: sin(AB)sinAsinB+sin(BC)sinBsinC+sin(CA)sinCsinA

We know that sin(α+β)=sinαcosβcosαsinβ

=sinAcosBcosAsinBsinAsinB+sinBcosCcosBsinCsinBsinC+sinCcosAcosCsinAsinCsinA

=sinAcosBsinAsinBcosAsinBsinAsinB+sinBcosCsinBsinCcosBsinCsinBsinC+sinCcosAsinCsinAcosCsinAsinCsinA

=cotBcotA+cosCcotB+cotAcotC

=0

= RHS

Hence proved.


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Principal Solution
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon