**Summary**

To solve trigonometric equations, several identities and formulas are used i.e:

For basic trigonometric equations, we follow the following steps to solve them:

1. Make sine, cosine or tangent the subject.

2. Use any method including a calculator to find basic angles.

3. Using quadrants, find all solutions in the given range.

#### Example #1

Q. Solve the equation for the range

*Solution:*

Using a calculator we can find that the basic angle

Now we know that cos is positive in the first quadrant and in the fourth quadrant hence another value of would be:

**Ans:**

#### Trigonometric Identities

Refer to Fig 1.

We know that:

Dividing 1 by 2 we get:

This is called an ”Identity”.

Using pythagoras theorem:

Dividing the whole equation by :

Substituting the values:

We get another identity:

where means ”equivalent to” or ”identical to”.

These identities are very useful when solving many trigonometric equations.

#### Example #2

Q. Prove the identity

*Solution:*

Taking left hand side only:

Take common:

Hence proven!

### Other trigonometric Formulas

Similarly, there are a few other formulas that help solve trigonometric equation: