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प्रश्न
tan2θ – sin2θ = tan2θ × sin2θ हे सिद्ध करण्यासाठी खालील कृती पूर्ण करा.
कृती: डावी बाजू = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= उजवी बाजू
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उत्तर
डावी बाजू = tan2θ – sin2θ
= `underline(tan^2theta) (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 -(underline(sin^2theta))/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/underline(sin^2theta))`
= `tan^2theta (1 - underline(cos^2theta))`
= tan2θ × sin2θ .....[1 – cos2θ = sin2θ]
= उजवी बाजू
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संबंधित प्रश्न
`(sin^2θ)/(cosθ) + cosθ = secθ`
`sqrt((1 - sinθ)/(1 + sinθ))` = secθ - tanθ
`1/(secθ - tanθ)` = secθ + tanθ
जर tanθ + `1/tanθ` = 2 तर दाखवा की `tan^2θ + 1/tan^2θ` = 2
`"tan A"/"cot A" = (sec^2"A")/("cosec"^2"A")` हे सिद्ध करा.
`(cos^2theta)/(sintheta) + sintheta` = cosec θ हे सिद्ध करा.
`sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ हे सिद्ध करा.
`(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ हे सिद्ध करा.
sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ हे सिद्ध करा.
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
