Q7 of 153 Page 7

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


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