Question

सिद्ध कीजिए। 

sec²θ + cosec²θ = sec²θ × cosec²θ   

Answer 1

बायाँ पक्ष = sec²θ + cosec²θ

`= 1/cos^2theta + 1/sin^2theta` ............`[because sectheta = 1/costheta, cosectheta = 1/sintheta]`

= `(sin^2theta + cos^2theta)/(cos^2theta.sin^2theta)`

= `1/(cos^2theta.sin^2theta)` ....`(because sin^2theta + cos^2theta = 1)`

= `1/cos^2theta xx 1/sin^2theta = sec^2theta xx cosec^2theta` .............`[because sectheta = 1/costheta, cosectheta = 1/sintheta]`

= दायाँ पक्ष

∴ बायाँ पक्ष = दायाँ पक्ष 

∴ sec²θ + cosec²θ = sec²θ × cosec²θ