1. Use the compound angle formulae to expand and simplify:

a
cos (60° + B)
b
tan (A + )
c
sin (A − 90°)

 

2. By expressing each angle as a sum or difference e.g. 75° = 45° + 30°, and using the special triangles, where necessary, evaluate as a surd:

a
cos 75°
b
tan 75°
c
sin 105°
d
cos 120°
e
sin 15°
f
tan 120°

3. Find the value of cos 2A if sin A = 0.4 and A is an acute angle.

4. Find the value of tan 2B if tan B = 1.5.

5. Write the following sums as products. i.e. Factorise

a
sin 45° + sin 30°
b
cos 60° − cos 45°
c
cos 60° + cos 30°
d
cos 7x + cos 3x
e
sin 4x + sin 2x
f
sin 5x − sin x

 

6. Write the following products as sums:

a
2 sin A sin 2B
b
2 sin 47°cos 23°
c
2cos 5θ cos 3θ
d
2 cos sin 
e
2 sin 5x / 2 sin 3x / 2
f
sin 3cos 2

7. Show that cos 2A = 1 − 2sin2 A

8. Write 2 cos 3D sin D as the sum of two trig functions.