TRIG/ALGEBRA
posted by cheyanne on .
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

1.
tan 15 = tan(4530)
= (tan45tan30)/(1 + tan45tan30)
= (1  1/√3)/(1 + 1/√3)
multiply by √3/√3
= (√31)/(√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