Question

sec²θ – cos²θ = tan²θ + sin²θ हे सिद्ध करा.

Answer 1

डावी बाजू = sec²θ – cos²θ

= sec²θ – (1 – sin²θ)    ......`[(because sin^2theta + cos^2theta = 1),(therefore 1 - sin^2theta = cos^2theta)]`

= sec²θ – 1 + sin²θ

= tan²θ + sin²θ     ......`[(because 1 + tan^2theta = sec^2theta),(therefore tan^2theta = sec^2theta - 1)]`

= उजवी बाजू

∴ sec²θ – cos²θ = tan²θ + sin²θ