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Question

Let cos(α+β)=45 and sin(αβ)=513 , where 0α, βπ4 , then tan2α is equal to

A
5633
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B
1912
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C
207
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D
2516
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Solution

The correct option is B 5633
tan2α=sin2αcos2α

tan2α=sin2α12sin22α

sin2α=sin[(α+β)+(αβ)]=sin(α+β)cos(αβ)+sin(αβ)cos(α+β)

=35×1213+513×45=3665+2065=5665

cos2α=12sin22α=12(5665)2=3365

tan2α=56653365=5633


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