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प्रश्न
सिद्ध करा:
cotθ + tanθ = cosecθ × secθ
उकल:
डावी बाजू = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
= उजवी बाजू
∴ cotθ + tanθ = cosecθ × secθ
उत्तर
डावी बाजू = 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
= उजवी बाजू
∴ cotθ + tanθ = cosecθ × secθ
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संबंधित प्रश्न
secθ + tanθ = `cosθ/(1 - sinθ)`
sinθ × cosecθ = किती?
`(sin θ - cos θ + 1)/(sin θ + cos θ - 1) = 1/(sec θ - tan θ)`
cosec θ.`sqrt(1 - cos^2theta) = 1` हे सिद्ध करा.
जर 1 – cos2θ = `1/4`, तर θ = ?
(sec θ + tan θ) . (sec θ – tan θ) = ?
sec2θ − cos2θ = tan2θ + sin2θ हे सिद्ध करा.
`"tan A"/"cot A" = (sec^2"A")/("cosec"^2"A")` हे सिद्ध करा.
`costheta/(1 + sintheta) = (1 - sintheta)/(costheta)` हे सिद्ध करा.
जर sin θ + cos θ = `sqrt(3)`, तर tan θ + cot θ = 1 हे दाखवा.
