# Trigonometric Functions-II, Further Applications of Addition and Subtraction Formula, Trigonometric Functions of Multiples of Angles

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## Further Applications of Addition and Subtraction Formula:

We shall prove that

(i)

(ii) or

Proof:

(i)

(ii)

Example:

Prove that

Solution:

L.H.S.

R.H.S.

Example:

Express the following products as a sum or difference

Solution:

## Trigonometric Functions of Multiples of Angles:

### (A) to Express Sin 2A in Terms of Sin a, Cos a and Tan A

We know that

By putting , we get

can also be written as

Dividing numerator and denominator by , we get

### (B) to Express Cos 2A in Terms of Sin a, Cos a and Tan A

We know that

Putting , we have

Also

i.e.,

Also

i.e.,

Dividing the numerator and denominator of R.H.S. by , we have

### (C) to Express Tan 2A in Terms of Tan A

Thus we have derived the following formulae:

, ,

Example:

Prove that .

Solution:

.