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Double-Angle and Half-Angle Formulas




 

In these lessons, we learn how to use the double angle formulas and the half-angle formulas to solve trigonometric equations and to prove trigonometric identities. We will also prove the double angle formulas and the half-angle formulas.

Related Topics:
More Lessons on Trigonometry, Trigonometry Worksheets, Trigonometry Games

The Double-Angle and Half-Angle Formulas are as follows:

Double Angle Formulas

sin 2a = 2 sin a cos a

cos 2a = cos 2a – sin 2a = 2 cos2a – 1 =  1 – 2 sin2a


Half Angle Formulas


Example:

Given , find
a) sin 2θ
b)

Solution:

a) sin 2θ = 2 sin θ cos θ

 




Using Double Angle Identities to Solve Equations

Using Double Angle Identities to Solve Equations, Example 1.
This video uses some double angle identities for sine and/or cosine to solve some equations.
1) cos(4x) − 3cos(2x) = 4
Using Double Angle Identities to Solve Equations, Example 2.
sin(2t) = sin(t)


 
Using Double Angle Identities to Solve Equations, Example 3
sin(2t) + 4sin(t) + 2cos(t) = −4

Prove Trigonometry Identities using Double Angles

Trigonometry Identities - Double Angles (1)
(1 − cos 2x)/sin 2x = tan x


Trigonometry Identities - Double Angle (2)
Prove tan x + cos x = 2 cosec 2x
Double-Angle Formulas
A few examples that use double-angle formulas from trigonometry.


 

Proof of the Double Angle Formulae

Trigonometry - Proof of the Double Angle Formulae.
The derivation of the double angle identities for sine and cosine, followed by some examples.


Using Half-Angle Formulas

Half-Angle Formulas
A few problems involving half-angle formulas in trigonometry.
Half Angle Identities to Evaluate Trigonometric Expressions, Example 1.
This video gives some half angle identities and shows how they can be used to solve some trigonometric equations.


 
Half Angle Identities to Evaluate Trigonometric Expressions, Example 2.
This video gives some half angle identities and shows how they can be used to solve some trigonometric equations.
Half Angle Identities to Evaluate Trigonometric Expressions, Example 2.
This video gives some half angle identities and shows how they can be used to solve some trigonometric equations.

Proof Half-Angle Formulas

This video derives the half angle trigonometry identities for cosine, sine and tangent.
Proof of the Half Angle Formula

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