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Question
sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ हे सिद्ध करा.
Solution
डावी बाजू = sin θ (1 – tan θ) – cos θ (1 – cot θ)
= `sintheta (1 - (sintheta)/(costheta)) - costheta (1 - (costheta)/(sintheta))`
= `sintheta - (sin^2theta)/costheta - costheta + (cos^2theta)/sintheta`
= `sintheta + (cos^2theta)/sintheta - (sin^2theta)/costheta - costheta`
= `(sin^2theta + cos^2theta)/sintheta - ((sin^2theta + cos^2theta)/costheta)`
= `1/sintheta - 1/costheta` ......[∵ sin2θ + cos2θ = 1]
= cosec θ – sec θ
= उजवी बाजू
∴ sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ
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खालील प्रश्नासाठी उत्तराचा योग्य पर्याय निवडा.
sec2θ – tan2θ = ?
जर cos θ = `24/25`, तर sin θ = ?
`(1 + sintheta)/(1 - sin theta)` = (sec θ + tan θ)2 हे सिद्ध करा.
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A हे सिद्ध करा.
sec2A – cosec2A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")` हे सिद्ध करा.
जर cos A = `(2sqrt("m"))/("m" + 1)`, असेल, तर सिद्ध करा cosec A = `("m" + 1)/("m" - 1)`
