# Trigonometric Functions of Sum and Difference of Two Angles

A. We shall learn the formulae

•  Changing y â†’ -y, we get

• Changing y â†’ x, in 1, 2, 3 we get

B. We shall arrive at some more formulae for cos 2x
Take the 8th formula â†’
This can be changed to a formula involving (1) only sin x or (2) only cos x.

C. We can also write these formulae for

D. Now we shall obtain the expansion for sin 3x, cos 3x and tan 3x using the  results we learnt above.

Example 1:

Solution:

Adding (1) & (2) We get

Example 2:
Find the value of without using tables.

Solution:

But sin Î¸ cannot be negative (Î¸ = 18Â° in the 1st quadrant)

2(a) Try these

Hint:- You can use the value of sin 18Â° already found and any relevant formula.

Example 3:

Solution:

Substituting in

Example 4:

Solution: