Trigonometric identities
Answers are for parents and teachers.
1
Prove the identity (1 + tan α)² + (1 − tan α)² = 2 : cos²α.
Expanding gives 2 + 2tan²α = 2(1 + tan²α) = 2 : cos²α.
2
Simplify (sin α − cos α)² + 2 sin α cos α.
1
3
Prove cos α : (1 + sin α) = (1 − sin α) : cos α.
Cross-multiplying gives cos²α = (1 − sin α)(1 + sin α) = 1 − sin²α, which is true.
4
Simplify tan α · cot α − sin²α.
cos²α
5
Compute sin² 37° + cos² 37° + tan 45°.
2