Question

prove that tan2
theta=2tan theta/1-tan^2theta​

Answer 1

Answer:

Explanation:

2tanθ1+tan2θ

= 2sinθcosθsec2θ

= 2sinθcosθ×1sec2θ

= 2sinθcosθ×cos2θ

= 2sinθcosθ

= sin2θ

Answer 2

$tan\ 2\theta = \frac{ 2\ tan\ \theta }{ 1 -tan^2\ \theta }$

Solution:

Given that,

We have to prove:

$tan\ 2\theta = \frac{ 2\ tan\ \theta }{ 1 -tan^2\ \theta }$

By addition formula of tan,

$tan(a+b) = \frac{tan\ a + tan\ b }{ 1-tan\ a\ tan\ b }$

Here,

$a = b = \theta$

Thus,

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

Thus proved

Learn more:

Prove that

tan2 theta/tan 2 theta-1 + cosec 2 theta/sec 2 theta - cosec 2 theta =1/sin 2 theta - cos2 theta

https://brainly.in/question/2680725

If cot b = 12/5. Prove that tan2 b - sin2 b = sin 4 b x sec2 b.

https://brainly.in/question/3276359