Question

cos(x+B)=cosxcosB-sinxsinB

Answer 1

[AI-generated answer — Explain Bot]

The given equation is cos(x + B) = cos(x)cos(B) - sin(x)sin(B).

To prove this equation, we can use the trigonometric identity called the angle sum identity for cosine.

The angle sum identity for cosine states that cos(A + B) = cos(A)cos(B) - sin(A)sin(B).

By comparing this identity with the given equation, we can see that A = x and B = B. So we can rewrite the given equation as:

cos(x + B) = cos(x)cos(B) - sin(x)sin(B)

This confirms that the given equation is indeed using the angle sum identity for cosine.

Therefore, to prove the given equation, you can directly substitute A = x and B = B into the angle sum identity for cosine and simplify the expression to show that both sides are equal.