Question

(sec θ - cos θ)(cot θ + tan θ) = tan θ sec θ

Answer 1

डावी बाजू = (sec θ - cos θ)(cot θ + tan θ)

= `(1/cos θ - cos θ) (cos θ/sin θ + sin θ/cos θ)`

= `((1 - cos^2θ)/cos θ)((cos^2θ + sin^2θ)/(sinθcosθ))`

= `sin^2θ/cosθ xx 1/(sinθcosθ)` ....`[(∵ sin^2θ + cos^2θ = 1),(∴ sin^2θ = 1 - cos^2θ)]` 

= `sinθ/cosθ . 1/cosθ`

= tan θ . sec θ

= उजवी बाजू

∴ (sec θ - cos θ)(cot θ + tan θ) = tan θ sec θ