Question

Simplify sin(a + b) / (cos(a) * cos(b)).

A. sin(a + b)
B. 1
C. sin(a) + sin(b)
D. cos(a) + cos(b)

Answer 1

The trigonometric expression sin(a + b) / (cos(a) * cos(b)) simplifies to tan(a) + tan(b). None of the options are correct.

Step-by-step explanation:

The question asked to simplify the expression sin(a + b) / (cos(a) * cos(b)). Using trigonometric identities, we know that sin(a + b) can be expressed as sin(a)cos(b) + cos(a)sin(b), according to the identity for the sine of the sum of two angles. Therefore, when we plug this into the original expression, it becomes:

(sin(a)cos(b) + cos(a)sin(b)) / (cos(a)cos(b))

When we divide term by term, we can see that both cos(b) in the numerator and cos(a) in the denominator will cancel each term respectively, leaving us with:

sin(a)/cos(a) + sin(b)/cos(b).

Both of these terms can be recognized as the tangent function, which provides us with:

tan(a) + tan(b).

Hence none of the options are correct.