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Question

Show that cot(A+B)=cotAcotB-1cotA+cotBA


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Solution

To prove: cot(A+B)=cotAcotB-1cotA+cotBA

Proof:

R.H.S=cotAcotB-1cotA+cotBA

=cosAsinAcosBsinB-1cosAsinA+cosBsinB

=cosAcosB-sinAsinBsinAsinBcosAsinB+sinAcosBsinAsinB

=cosAcosB-sinAsinBsinAsinB×sinAsinBcosAsinB+sinAcosB

=cosAcosB-sinAsinBcosAcosB+sinAsinB

=cos(A+B)sin(A+B)

=cot(A+B)

⇒L.H.S=R.H.S

Hence proved


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