Question

1/cosec theta+cos theta - 1/sintheta=1/sintheta-1/cosectheta-cottheta​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\dfrac{1}{cosec(\theta)+cot(\theta)}-\dfrac{1}{sin(\theta)}}$

$\sf{=\dfrac{cosec^2(\theta)-cot^2(\theta)}{cosec(\theta)+cot(\theta)}-cosec(\theta)}$

$\sf{=\dfrac{\{cosec(\theta)-cot(\theta)\}\{cosec(\theta)+cot(\theta)\}}{cosec(\theta)+cot(\theta)}-cosec(\theta)}$

$\sf{=cosec(\theta)-cot(\theta)-cosec(\theta)}$

$\sf{=cosec(\theta)-\{cosec(\theta)+cot(\theta)\}}$

$\sf{=\dfrac{1}{sin(\theta)}-\bigg\{\dfrac{cosec(\theta)+cot(\theta)}{cosec^2(\theta)-cot^2(\theta)}\bigg\}}$

$\sf{=\dfrac{1}{sin(\theta)}-\bigg\{\dfrac{cosec(\theta)+cot(\theta)}{(cosec(\theta)-cot(\theta))(cosec(\theta)+cot(\theta))}\bigg\}}$

$\sf{=\dfrac{1}{sin(\theta)}-\dfrac{1}{cosec(\theta)-cot(\theta)}}$