Question

Cot theta+Cosec theta-1/ Cot theta-Cosec theta+1=?​

Answer 1

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

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

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

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

$= (Cotθ + Cosecθ)$

Answer 2

Answer:

=Cotθ−Cosecθ+1Cotθ+Cosecθ−1

= \displaystyle \: \frac{Cotθ + Cosecθ - ( {Cosec}^{2}θ - {Cot}^{2}θ) }{Cotθ + 1 - Cosecθ}=Cotθ+1−CosecθCotθ+Cosecθ−(Cosec2θ−Cot2θ)

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

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

= (Cotθ + Cosecθ)=(Cotθ+Cosecθ)