Question

cot theta +cosec theta - 1 \ cot theta - cosec theta + 1 = 1 + cos theta \ sin theta
​

Answer 1

Step-by-step explanation:

Hope u get the Answer. hence LLS=RHS PROVED

Answer 2

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

$\displaystyle \: \frac{Cotθ + Cosecθ - 1}{Cotθ - Cosecθ + 1}$

$= \displaystyle \: \frac{Cotθ + Cosecθ - ( {Cosec}^{2}θ - {Cot}^{2}θ) }{Cotθ + 1 - Cosecθ}$

$= \frac{(Cotθ + Cosecθ )-(Cosecθ + Cotθ )(Cosecθ - Cotθ) }{Cotθ + 1 - Cosecθ}$

$= \frac{(Cotθ + Cosecθ )(Cotθ + 1 - Cosecθ)}{(Cotθ + 1 - Cosecθ)}$

$= (Cotθ + Cosecθ)$

$= \displaystyle \: \frac{1 + cos \theta}{sin \theta}$