Question

If θ is an acute angle and 3 tan2 θ -1 = 0, find cos 2θ.

Answer 1

Answer:

Step-by-step explanation:

First, find out the value of $\theta$.

$3tan^{2}\theta = 1\\tan^{2}\theta = \frac{1}3\\tan\theta = \sqrt{\frac{1}3}\\tan\theta = \frac{1}{\sqrt{3}}$

Following the trigonometric values of certain angles,

$tan30 = \frac{1}{\sqrt{3}}$

∴ $tan\theta = tan30$

∴ θ = 30°

Now, substitute the value of θ in $cos^{2}\theta$

$cos^{2}\theta\\= cos^{2}30\\= (cos30)^{2}\\= (\frac{\sqrt{3}}{2})^{2}\\= \frac{3}4$

The values of certain angles is given below. Refer to the attachment for your convenience. Be sure to remember all of them.