Question

सिद्ध कीजिए। 

tan⁴θ + tan²θ = sec⁴θ - sec²θ 

Answer 1

बायाँ पक्ष = tan⁴θ + tan²θ

= `tan^2theta(tan^2theta + 1)`

= `tan^2theta xx sec^2theta` ......`[∵ 1 + tan^2theta = sec^2theta]`

= `(sec^2theta - 1) xx sec^2theta` .........`[(∵ 1 + tan^2theta = sec^2theta),(∴ sec^2theta - 1 = tan^2theta)]`

= `sec^4theta - sec^2theta`

= दायाँ पक्ष

∴ बायाँ पक्ष = दायाँ पक्ष

∴ tan⁴θ + tan²θ = sec⁴θ - sec²θ