Question

# Assertion :sin(A+B)+sin(Aâˆ’B)cos(A+B)+cos(Aâˆ’B)=tanA Reason: sin(A+B)+sin(Aâˆ’B)=sinA and cos(A+B)+cos(Aâˆ’B)=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 incorrectReason is false assin(A+B)+sin(A−B)=2sin((A+B)+(A−B)2)cos((A+B)−(A−B)2)=2sinAcosBAndcos(A+B)+cos(A−B)=2cos((A+B)+(A−B)2)cos((A+B)−(A−B)2)=2cosAcosBAssertion is true assin(A+B)+sin(A−B)cos(A+B)+cos(A−B)=2sinAcosB2cosAcosB=sinAcosA=tanA

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