Trig Identities

Question 1

Addition Formulas (4)

Answer 1

1) sin (a + b) = sin a cos b + cos a sin b
2) sin (a - b) = sin a cos b - cos a sin b
3) cos (a + b) = cos a cos b - sin a sin b
4) cos (a - b) = cos a cos b + sin a sin b

Question 2

Double-Angle Formulas (2)

Answer 2

1) sin 2x = 2 sin x cos x
2) cos 2x = 1 -2 sin² x

Question 3

Half-Angle Formulas (2)

Answer 3

1) sin² x = 1/2 - 1/2 cos 2x
2) cos² x = 1/2 + 1/2 cos 2x

Question 4

Product to Sum Formulas (4)

Answer 4

1) cos a cos b = 1/2 (cos (a + b) + cos (a - b))
2) sin a sin b = 1/2 (cos (a - b) - cos (a + b))
3) sin a cos b = 1/2 (sin (a + b) + sin (a - b))
4) cos a sin b = 1/2 (sin (a + b) - sin (a - b))

Question 5

√a²-x²

Answer 5

x = a sin u

√a²-x² = a cos u

Question 6

√a²+x²

Answer 6

x= a tan u

√a²+x² = a sec u

Question 7

√x²-a²

Answer 7

x= a sec u

√x²-a² = a tan u