Question

prove that tan theta/root 1+tan^2 theta = sin theta

Answer 1

1+tan^2 theta=sec^2 theta is a formula and 1/sec theta =cos theta

Answer 2

We need to recall the following trigonometric formulas.

• $1+tan^{2}\theta =sec^{2}\theta$
• $sec\theta=\frac{1}{cos\theta}$
• $tan\theta=\frac{sin\theta}{cos\theta}$

This problem is about trigonometry.

Given:

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

To prove the above trigonometric equation, consider

$\frac{tan\theta}{\sqrt{1+tan^2\theta} }$

$=\frac{tan\theta}{\sqrt{sec^2\theta} }$

$=\frac{tan\theta}{{sec\theta} }$

$=\frac{sin\theta}{cos\theta}*\frac{1}{sec\theta}$

$=\frac{sin\theta}{cos\theta}*{cos\theta}$

$=sin\theta$

Hence, proved.