Question

1) Find the exact value. Use a sum or difference identity.
tan (-15 degrees)


2) Rewrite the following expression as a trigonometric function of a single angle measure.

cos 3x cos 4x - sin 3x sine 4x

Answer 1

1.
tan 15 = tan(45-30)
= (tan45-tan30)/(1 + tan45tan30)
= (1 - 1/√3)/(1 + 1/√3)
multiply by √3/√3
= (√3-1)/(√3+1)
but tan(-15) = -tan15
so
tan(-15°) = (1-√3)/(√3 + 1)


cos 3x cos 4x - sin 3x sine 4x
= cos(3x+4x) = cos 7x