Question

सिद्ध कीजिए। 

sec²θ + cosec²θ = sec²θ × cosec²θ   

Answer 1

बायाँ पक्ष = sec²θ + cosec²θ

${\displaystyle =\frac{1}{{\cos }^2\theta }+\frac{1}{{\sin }^2\theta }}$ ............${\displaystyle [\because \sec \theta =\frac{1}{\cos \theta },\cos ec\theta =\frac{1}{\sin \theta }]}$

= ${\displaystyle \frac{{\sin }^2\theta +{\cos }^2\theta }{{\cos }^2\theta .{\sin }^2\theta }}$

= ${\displaystyle \frac{1}{{\cos }^2\theta .{\sin }^2\theta }}$ ....${\displaystyle (\because {\sin }^2\theta +{\cos }^2\theta =1)}$

= ${\displaystyle \frac{1}{{\cos }^2\theta }\times \frac{1}{{\sin }^2\theta }={\sec }^2\theta \times \cos e{c}^2\theta }$ .............${\displaystyle [\because \sec \theta =\frac{1}{\cos \theta },\cos ec\theta =\frac{1}{\sin \theta }]}$

= दायाँ पक्ष

∴ बायाँ पक्ष = दायाँ पक्ष 

∴ sec²θ + cosec²θ = sec²θ × cosec²θ