Identities of Doubled Angles

Practice Questions

Trigonometry › Identities of Doubled Angles

Questions

10

1

Simplify the function below:

$f\left ( x\right ) = \frac{\cos^2x - \sin^2 x}{1 - \cos^2 x}$

2

Given $\sin \left ( x\right ) = a$ , what is $\cos \left ( 2x\right )$ in terms of ?

3

Using trigonometric identities, determine whether the following is valid:

$\frac{2\cos A}{1 - \cos 2A} = \csc A \cot A$

4

Using trigonometric identities determine whether the following is true:

$\csc A \sec A = \frac{2}{\sin 2A}$

5

Using a double angle formula, find the value of

$\sin \left(2*\frac{\pi}{3}\right)$ .

6

Find the value of $cos(2\theta)$ if $sin(\theta)= \frac{2}{3}$ , and if the value of is less than zero.

7

Suppose is an angle in the third quadrant, such that:

$tan\ X = 0.83$

What is the value of $cos\ 2X$ ?

8

What is the period of $f(x) = 2sin(\pi x)cos(\pi x)$ ?

9

Expand the following expression using double-angle identities.

$\sin 4x$

10

Simplify the function below:

$f\left ( x\right ) = \frac{1}{\cos^2x} - \frac{1-\cos2x}{1 + \cos2x}$

Return to subject