# Trigonometric Ratios of Multiple Angles

## Trigonometric Ratios of Multiple Angles

If A is an angle, then 2A, 3A, 4A, 5A, etc are called multiple angles of A. In this section we will discuss about the trigonometric ratios of multiple angles 2A and 3A in terms of A.

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### Geometrical Proof of 2A Formulae

Let O be the centre of the circle ABC and AB be a diameter (In the given figure below.). Let CAB = A, then COB = 2A [ Central angle is double of inscribed angle on same arc.]. ACB = 90° [Inscribed angle on semi-circle.]

Let CM is perpendicular to AB. Then, ACM = 90° – A, and hence BCM = A.

Now from the right angle Î”OMC,

### Worked Out Examples:

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