Question

Simplify in terms of sine and cosine
(1+tanθ)^2−2tanθ

Answer 1

Explanation:

Recall the Identity:

`\tan(2\theta) = (2tan(\theta))/(1 -\tan(\theta)^2)`

Let's r rewrite the Identity:

`\tan(2\theta) = (2\tan(\theta))/(1-\tan(\theta)^2) \\ \tan(2\theta) * (1-\tan(\theta)^2) = (2\tan(\theta))/(1-\tan(\theta)^2) * (1-\tan(\theta)^2) \\ \tan(2\theta)(1-\tan(\theta)^2) = 2\tan(\theta) \\ (\tan(2\theta)(1 -\tan(\theta)^2))/(\tan(2\theta)) = (2\tan(\theta))/(\tan(2\theta)) \\ 1-\tan(\theta)^2 = (2\tan(\theta))/(\tan(2\theta))`