Question

सिद्ध कीजिए। 

(secθ - cosθ)(cotθ + tanθ) = tanθ secθ 

Answer 1

बायाँ पक्ष = (secθ - cosθ)(cotθ + tanθ)

= `(1/costheta - costheta)(costheta/sintheta + sintheta/costheta)` ...............`[sectheta = 1/costheta, cottheta = costheta/sintheta और tantheta = sintheta/costheta]` 

= `((1 - cos^2theta)/(costheta))((cos^2theta + sin^2theta)/(sintheta.costheta))` 

= `sin^2theta/costheta xx 1/(sintheta.costheta)`  .................`[(∵ sin^2theta + cos^2theta = 1),(∴ sin^2theta = 1 - cos^2theta)]`

= `sintheta/costheta xx sintheta xx 1/sintheta xx 1/costheta`

= `sintheta/costheta xx 1/costheta`

= `tantheta xx sectheta` ........`[∵ sintheta/costheta = tantheta, 1/costheta = sectheta]`

= दायाँ पक्ष

∴ बायाँ पक्ष = दायाँ पक्ष

∴ (secθ - cosθ)(cotθ + tanθ) = tanθ secθ.