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Question
sec θ(1 - sin θ) (sec θ + tan θ) = 1
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Solution
डावी बाजू = sec θ(1 - sin θ) (sec θ + tan θ)
= `1/cos θ(1 - sin θ)(1/cos θ + sin θ/cos θ)`
= `(1 - sin θ)/cos θ((1 + sin θ)/cos θ)`
= `(1 - sin^2θ)/(cos^2θ)`
= `(cos^2θ)/(cos^2θ)` ..........`[(∵ sin^2θ + cos^2θ = 1), (∴ 1 - sin^2θ = cos^2θ)]`
= 1
= उजवी बाजू
∴ sec θ(1 - sin θ) (sec θ + tan θ) = 1
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sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ हे सिद्ध करा.
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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
θ चे निरसन करा:
जर x = r cosθ आणि y = r sinθ
