Question

if cosec theta + cot theta = m show that m2-1/m2+1 = cos theta

Answer 1

old but good question

Answer 2

Answer:

Step-by-step explanation:

It is given that $cosec{\theta}+cot{\theta}=m$, then

$\frac{1}{sin{\theta}}+\frac{cos{\theta}}{sin{\theta}}=m$

$\frac{1+cos{\theta}}{sin{\theta}}=m$

$(\frac{1+cos{\theta}}{sin{\theta}})^2=m^2$

$m^2=\frac{1+cos^2{\theta}+2cos{\theta}}{sin^2{\theta}}$

Now, $\frac{m^2-1}{m^2+1}=\frac{1+cos^2{\theta}+2cos{\theta}-sin^2{\theta}}{1+cos^2{\theta}+2cos{\theta}+sin^2{\theta}}$

$\frac{m^2-1}{m^2+1}=\frac{2cos^2{\theta}+2cos{\theta}}{2+2cos{\theta}}$

$\frac{m^2-1}{m^2+1}=cos{\theta}$

Hence proved.