Find the EXACT value of
sin(A−B) if cos A = 3/5 where A is in Quadrant IV and cos B = 12/13
where B is in Quadrant IV. Assume all angles are measured from standard position.

Step-by-step explanation:

step 1

Find the value of sin(A)

we know that

we have

substitute

Remember that the angle A is in Quadrant IV

so

The value of sin(A) is negative

therefore

step 2

Find the value of sin(B)

we know that

we have

substitute

Remember that the angle B is in Quadrant IV

so

The value of sin(B) is negative

therefore

step 3

Find the value of sin(A-B)

we know that

substitute the given values

(a) the volume of the cone is 20/3 in3

hence, option a is correct.