Using the fact that sin(A+B)=sin A cos B + cos A sin B and differentiation,

obtain the sum formula for cosines.

Open in App

Solution

Using sin (A+B) = sin A cos B + cos A sin B, we have on differentiating w.r.t. x, regarding B as constant and consider A as a formula of x, we have

$c o s (A + B) \frac{d A}{d x} = c o s B . c o s A \frac{d A}{d x} - (s i n A \frac{d A}{d x}) s i n B \Rightarrow c o s (A + B) \frac{d A}{d x} = (c o s A c o s B - s i n A s i n B) \frac{d A}{d x} \Rightarrow c o s (A + B) = c o s A c o s B - s i n A s i n B (∵ \frac{d A}{d x} \neq 0)$

Suggest Corrections

Similar questions

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

If sin(A - B) = sinA cos B - cosA sinB and cos(A - B)= cos A cos B + sin Asin B then find
sin15 and cos 15 .

sin (A - B) = sin A cos B - cos A sin B

sin 15^{o}

Join BYJU'S Learning Program