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  • Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.

 Q20 Using the fact that \sin (A + B) = \sin A \cos B + \cos A \sin B and the differentiation,
         obtain the sum formula for cosines.

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best_answer

Given function is
\sin (A + B) = \sin A \cos B + \cos A \sin B
Now, differentiate w.r.t. x
\frac{d(\sin(A+B))}{dx} = \frac{d\sin A}{dx}.\cos B+\sin A.\frac{d\cos B}{dx}+\frac{d\cos A}{dx}.\sin B+\cos A.\frac{d\sin B}{dx}
\cos (A+b)\frac{d(A+B)}{dx}     =\frac{dA}{dx}(\cos A\cos B-\sin A\cos B)+\frac{dB}{dx}(\cos A \sin B-\sin A\sin B) 
                                                =(\cos A \sin B-\sin A\sin B).\frac{d(A+B)}{dx}
\cos(A+B)= \cos A\sin B-\sin A\cos B
Hence, we get the formula by differentiation of sin(A + B)                            



                                               

Posted by

Gautam harsolia

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