Sin2x Formula

Trigonometric formulas like Sin2x, Cos 2x, Tan 2x are known as double-angle formulae. To understand it better, It is important to go through the practice examples provided.

This article will let you understand the concept of: 

Derive the double-angle formulae using the addition formulae.

Write trigonometric expressions in other forms using the formulae

Use the formulae for the solution of trigonometric equations

Formula: Sin 2 X = 2SinX Cos X

The sin 2 θ formula Introduction.

Here we find trigonometric formulae known as double angle formulae. So, the name is double angle formula because it comprises a function of double angles - that is, sin 2x

Deriving Double Angle Formulae for Sin 2 

We start off by remembering the addition formula to find Sine double-angle formula 

sin(A + B) = sin A cos B + cos A sin B 

Double Angle formula to get 2sinxcosx

Now let's see what happens when we let B equal to A.

After doing so, the first of these formulae becomes sin(x + x) = sin x cos x + cos x sin x

So that sin2x = 2 sin x cos x.

And this is our first double-angle formula, so called because we are doubling the angle (as in 2A).

Examples for sin 2x

If we want to solve the following equation:

Sin 2x = sinx, -Π ≤ Π

We will follow the following steps:

Step 1: Use the Double angle formula

Sin 2x = 2 Sin x Cos x

Step 2: Let's rearrange it and factorize

2Sinx Cosx – sinx = 0

Sin x(2 cos x -1) = 0

So, a) Sinx =0

or

b) cos2x -1 = 0

Step 3: Let's consider Sin x = 0. (Refer to the graph)

We have two solutions as x = Π & x = 0.

Step 4: x = Π will be excluded as it isn't in the interval mentioned in the question .

Step 5: from equation b, 2cosx -1 = 0

2 cos x = 1

Cos x =½

Cos x = 600 or Π/3

Step 6: By looking at the graph, we can conclude that

x = – Π/3 & x = Π/3

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