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Question

Whether the given equation sinBsinA=sin(2A+B)sinA−2cos(A+B) ?

A
True
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B
False
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Solution

The correct option is A True
R.H.S

sin(2A+B)sinA2cos(A+B)

=sin(A+A+B)sinA2cos(A+B) [as sin(A+B)=sinAcosB+cosC]

=sinAsin(A+B)+cosAsin(A+B)2sinAcosBsinA

=sinAcos(A+B)+cosAsin(A+B)sinA

=sin(A+B)cosAcos(A+B)sinAsinA[(A+B)=sinAcosBcosC]

=sin(A+BA)sinA=sinBsinA=(L.H.S) (proved)

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