Question

if tan2Theta=3SinTheta CosTheta then TanTheta will be

Answer 1

Answer:

Step-by-step explanation:

We have,

$\sf{tan(2\theta)=3\,sin(\theta)\,cos(\theta)}$

$\sf{\implies\,\dfrac{sin(2\theta)}{cos(2\theta)}=3\,sin(\theta)\,cos(\theta)}$

$\sf{\implies\,\dfrac{2\,sin(\theta)\,cos(\theta)}{cos(2\theta)}=3\,sin(\theta)\,cos(\theta)}$

$\sf{\implies\,\dfrac{2}{cos(2\theta)}=3}$

$\sf{\implies\,\dfrac{2}{3}=cos(2\theta)}$

$\sf{\implies\,2\,cos^2(\theta)-1=\dfrac{2}{3}}$

$\sf{\implies\,2\,cos^2(\theta)=1+\dfrac{2}{3}}$

$\sf{\implies\,2\,cos^2(\theta)=\dfrac{3+2}{3}}$

$\sf{\implies\,2\,cos^2(\theta)=\dfrac{5}{3}}$

$\sf{\implies\,cos^2(\theta)=\dfrac{5}{6}}$

$\sf{\implies\,sec^2(\theta)=\dfrac{6}{5}}$

$\sf{\implies\,tan^2(\theta)+1=\dfrac{6}{5}}$

$\sf{\implies\,tan^2(\theta)=\dfrac{6}{5}-1}$

$\sf{\implies\,tan^2(\theta)=\dfrac{6-5}{5}}$

$\sf{\implies\,tan^2(\theta)=\dfrac{1}{5}}$

$\sf{\implies\,tan(\theta)=\pm\dfrac{1}{\sqrt{5}}}$