Question

If coseco + coto = p. then the value of​

Answer 1

cosecθ+cotθ=p then cosθ=3

∴cosec2θ−cot2θ=1

(cosecθ−cotθ)(cosecθ+cotθ)=1

(cosecθ−cotθ)⋅P=1

cosecθ−cotθ=P1(i)

Given cosecθ+cotθ=P(ii)

Equation (i) + Equation (ii)

⇒cosecθ−cotθ=P1

       cosecθ+cotθ=P

_______________________________________

⇒2cosecθ=P1+P

_______________________________________

⇒cosecθ=2P1+P2

⇒sinθ1=2P1+P2

Square in both sides

⇒sin2θ=(1+P2)2(2P)2         [∵sin2θ=1−cos2θ]

⇒1−cos2θ=1+P4+2P24P2

⇒1−1+P4+2P24P2=cos2θ

⇒1+P4+2P21+P4+2P2−4P2=cos2θ

⇒1+P4+2P21+P4−2P2=cos2θ

⇒(1+P2)2(1−P2)2