Question

If $\sec \theta +\tan \theta =p,$ then find the value of $co\sec \theta$

Answer 1

$sec\theta +tan\theta =P.$

$\Rightarrow \frac{1+sin\theta }{cos\theta }=P.\Rightarrow \frac{(1+sin\theta {)}^2}{1-sin\theta }=P^2$

$\Rightarrow \frac{1+sin\theta }{1-sin\theta }=P^2\Rightarrow 1+sin\theta =P^2-P^{2}sin\theta .$

$\Rightarrow (1+P^2)sin\theta =P^2-1\Rightarrow cosec\theta =\frac{1+P^2}{P^2-1}$