Sums and differences of sines and cosines
Answers are for parents and teachers.
1
Compute cos 75° + cos 15°.
√6/2
2
Convert sin 5α − sin α into a product.
2 sin 2α cos 3α
3
Convert cos 7α − cos 3α into a product.
−2 sin 5α sin 2α
4
Compute sin 70° − sin 10°.
cos 40°
5
Prove (sin 3α + sin α) : (cos 3α + cos α) = tan 2α.
The numerator is 2 sin 2α cos α, the denominator 2 cos 2α cos α; cancelling gives sin 2α : cos 2α = tan 2α.