Question

If sec theta + tan theta = p
then find the value of cosec theta​
​

Answer 1

sec θ + tan θ = p,

(1/cosθ)+(sinθ/cosθ)=p

(1+sinθ)/cosθ=p

squaring both sides gives

(1+sinθ)²/cos²θ=p²

(1+sinθ)²/(1-sin²θ)=p²

(1+sinθ)( 1+sinθ)/{(1+sinθ )(1-sinθ )}=p²

(1+sinθ)/(1-sinθ )=p²

1+sinθ =p²(1-sinθ )

1+sin θ =p² -p²sinθ

sin θ -p²sinθ=p² -1

sinθ(1 -p²)=(p² -1)

Hence sin θ=(p² -1)/(1 -p²)

and cosecθ =1/sin θ =(1 -p²)/(p² -1)