**Trigonometric Ratios of Multiple Angles**

If ** A** is an angle, then

**,**

*2A***,**

*3A***,**

*4A***, etc are called**

*5A***multiple angles**of

**. In this section we will discuss about the**

*A***trigonometric ratios of multiple angles**

**and**

*2A***in terms of**

*3A***.**

*A***Trigonometric Ratios of Angle 2A in terms of A**

**Formula for sin2A**

**Formula for cos2A**

**Formula for tan2A and cot2A**

**Some Useful Results**

**Trigonometric Ratios of Angle 3A in terms of A**

**List of trigonometric formula for multiple angles 2A and 3A:**

**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:*

*Worked Out Examples:*

*You can comment your questions or problems regarding the
trigonometric ratios of multiple angles.*

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