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Question

Prove that:
(i) 1sin(xa)sin(xb)=cot(xa)cot(xb)sin(ab)
(ii) 1sin(xa)cos(xb)=cot(xa)+tan(xb)cos(ab)

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Solution

=1sin(ab)=1sin(ab)[sin(xb)(xa)cos(xa)cos(xb)]=1sin(ab)=[sin(xb)cos(xa)cos(xb)sin(xa)cos(xa)cos(xb)cos(xa)cos(xb)]=1sin(ab)[sin(xb)cos(xb)sin(xa)cos(xa)]=1sin(ab)[tan(xb)tan(xs)]=tan(xb)tan(xa)sin(ab)
= RHS
LHS = RHS Hence proved.


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