Question

prove that cot theta + cosec theta minus one upon cot theta minus cosec theta minus 1 is equals to 1 + cos theta upon sin theta

Answer 1

Proof Is given in the enclose file

Thank You

Answer 2

Answer with step-by-step explanation:

To Prove  : $\dfrac{cot\theta + cosec\theta -1 }{cot\theta - cosec\theta +1} = \dfrac{1+cos\theta}{sin\theta}$

$L.H.S= \dfrac{cot\theta + cosec\theta -1 }{cot\theta - cosec\theta +1}\\\\\\= \dfrac{cot\theta + cosec\theta -(cosec^2\theta-cot^2\theta) }{ cosec\theta- cot\theta+1}\\\\\\= \dfrac{cot\theta + cosec\theta -(cosec\theta +cot\theta )(cosec\theta -cot\theta ) }{cot\theta - cosec\theta +1}\\\\\\= \dfrac{(cot\theta + cosec\theta)(1 -(cosec\theta-cot\theta))}{cot\theta - cosec\theta +1}\\\\\\cot\theta+cosec\theta=\dfrac{cos\theta}{sin\theta} + \dfrac{1}{sin\theta} =\dfrac{1+cos\theta}{sin\theta} = R.H.S.$

Hence, proved