Write the value of cosec2 (90° − θ) − tan2θ.
To find: cosec2 (90° − θ) − tan2θ
∵ cosec (90° – θ) = sec θ
∴ cosec2 (90° – θ) = sec2 θ
⇒ cosec2 (90° θ) − tan2 θ = sec2 θ – tan2 θ
Now, ∵ 1 + tan2 θ = sec2 θ
∴ cosec2 (90° − θ) − tan2 θ = sec2 θ – tan2 θ
= 1 + tan2 θ – tan2 θ = 1