As you know there are these trigonometric formulas like Sin 2x, Cos 2x, Tan 2x which are known as double angle formulae for they have double angles in them. To get a good understanding of this topic, Let’s go through the practice examples provided.

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## Introduction to Cos 2 Theta formula

Let’s have a look at trigonometric formulae known as the double angle formulae. They are said to be so as it involves double angles trigonometric functions, i.e. Cos 2x.

### Deriving Double Angle Formulae for Cos 2t

Let’s start by considering the addition formula.

Cos(A + B) = Cos A cos B – Sin A sin B

Let’s equate B to A, i.e A = B

And then, the first of these formulae becomes: Cos(t + t) = Cos t cos t – Sin t sin t

so that Cos 2t = Cos2t – Sin2t

And this is how we get second double-angle formula, which is so called because you are doubling the angle (as in 2A).

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## Practice Example for Cos 2:

Solve the equation cos 2a = sin a, for – Π
$$\begin{array}{l}\leq\end{array}$$
a2 a

It becomes 1 − 2 sin2 a = sin a

2 sin2 a + sin a − 1=0,

Let’s factorise this quadratic equation with variable sinx

(2 sin a − 1)(sin a + 1) = 0

2 sin a − 1 = 0 or sin a + 1 = 0

sin a = 1/2 or sin a = −1

To check other mathematical formulas and examples, visit BYJU’S.

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