9.24 Doubleangle identities
Doubleangle identities
In this lesson, we will learn how to make use of the doubleangle identities, a.k.a. doubleangle formulas to find the sine and cosine of a double angle. It’s hard to simplify complex trigonometric functions without these formulas.
Basic concepts:
 Using sine ratio to calculate angles and side (Sin = $\frac{o}{h})$
 Using cosine ratio to calculate angles and side (Cos = $\frac{a}{h}$)
 Using tangent ratio to calculate angles and side (Tan = $\frac{o}{a} )$
 Trigonometric ratios of angles in radians
Related concepts:
 Solving trigonometric equations using doubleangle identities
Lessons
Notes:
Download the Trigonometry identities chart here
Formulas:$\sin 2\theta = 2\sin x\cos x$
$\cos 2 \theta = {\cos ^2}x  {\sin^2}x$
$= \;2{ \cos ^2}x  1$
$= \;1  2{\sin ^2}x$
$\tan 2 \theta = {{2\tan x} \over {1  \tan ^2}x}$

1.
Express each of the following in terms of a single trigonometric function:

2.
Prove identities

a)
$\sin 2x$

b)
$\sec 2x$

c)
$\tan 2x$
