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Question

Prove that :(sin55sin19)+(sin53sin17)=cos1

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Solution

Lets take LHS and then equate it to RHS

LHS =(sin55sin19)+(sin53sin17)

=(sin55+sin53)(sin19+sin17)

=2sin(54)cos12sin(18)cos1) [sinC+sinD=2sin(C+D2)cos(CD2)]

=2cos1[sin54sin(18]

=2cos1[2cos36sin18] [sinCsinD=2cos(C+D2)sin(CD2)]

=2cos1[2(5+14)(514)]

=cos1×(5)2124

=cos1

= RHS

(sin55sin19)+(sin53sin17)=cos1


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