Question

सिद्ध कीजिए: cotθ + tanθ = cosecθ × secθ

हल:

बायाँ पक्ष = cotθ + tanθ

= `cosθ/sinθ + sinθ/cosθ`

= `(square + square)/(sinθ xx cosθ)`

= `1/(sinθ xx cosθ)` ............... `square`

= `1/sinθ xx 1/square`

= cosecθ × secθ

∴ बायाँ पक्ष = दायाँ पक्ष

∴ cotθ + tanθ = cosecθ × secθ

Answer 1

बायाँ पक्ष = cotθ + tanθ

= `cosθ/sinθ + sinθ/cosθ`

= `(bb(cos^2theta + sin^2theta))/(sinθ xx cosθ)`

= `1/(sinθ xx cosθ)` ............... `bb([sin^2theta + cos^2theta = 1])`

= `1/sinθ xx 1/bbcostheta`

= cosecθ × secθ

∴ बायाँ पक्ष = दायाँ पक्ष

∴ cotθ + tanθ = cosecθ × secθ