Question

Prove that (tan theta / sec theta -1 ) + (tan theta / sec theta + 1) = 2 cosec theta

Answer 1

this is the solution for your question

Answer 2

Answer:

Step-by-step explanation:

The given equation is:

$\frac{tan{\theta}}{sec{\theta}-1}+\frac{tan{\theta}}{sec{\theta}+1}=2cosec{\theta}$

Taking the LHS of  the above equation,  

$\frac{tan{\theta}}{sec{\theta}-1}+\frac{tan{\theta}}{sec{\theta}+1}$

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

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

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

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

=$2sec{\theta}cot{\theta}$

=$2{\times}\frac{1}{cos{\theta}}{\times}\frac{cos{\theta}}{sin{\theta}}$

=$\frac{2}{sin{\theta}}$

=$2cosec{\theta}$=RHS

Hence proved.