Question

Simplify the expression by using a double-angle formula or a half-angle formula. (a) 2 tan(5°) 1 − tan2(5°)

Answer 1

The question is related to trigonometry and we have to use the formula of double angle .

Here we use double angle formula of tangent function which is

$tan(2x) = \frac{2tan(x)}{1-tan^2(x)}$

Given expression is

$\frac{2tan (5 \degree)}{1-tan^2(5 \degree)}$

Comparing it with double angle formula, we will get x = 5

SO the required expression is equal to

$\frac{2tan (5 \degree)}{1-tan^2(5 \degree)} =tan(2*5 )$

$\frac{2tan (5 \degree)}{1-tan^2(5 \degree)} =tan(10 )$

So the answer is tan(10) .