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Assertion :sin(A+B)+sin(AB)cos(A+B)+cos(AB)=tanA Reason: sin(A+B)+sin(AB)=sinA and cos(A+B)+cos(AB)=cosA

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is C Assertion is correct but Reason is incorrect
Reason is false as

sin(A+B)+sin(AB)

=2sin((A+B)+(AB)2)cos((A+B)(AB)2)

=2sinAcosB

And

cos(A+B)+cos(AB)

=2cos((A+B)+(AB)2)cos((A+B)(AB)2)

=2cosAcosB

Assertion is true as

sin(A+B)+sin(AB)cos(A+B)+cos(AB)=2sinAcosB2cosAcosB=sinAcosA=tanA

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