Question

if cosec a +cot a =mshow that m^2-1/m^2+1 =cos a​

Answer 1

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}}

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