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प्रश्न
`sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ हे सिद्ध करा.
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उत्तर
डावी बाजू = `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)`
= `sintheta/(1/costheta + 1) + sintheta/(1/costheta - 1`
= `sintheta/((1 + costheta)/costheta) + sintheta/((1 - costheta)/(costheta))`
= `(sintheta costheta)/(1 + costheta) + (sintheta costheta)/(1 - costheta)`
= `sin theta costheta (1 /(1 + costheta) + 1/(1 - costheta))`
= `sintheta costheta [(1 - costheta + 1 + costheta)/((1 + costheta)(1 - costheta))]`
= `sintheta costheta (2/(1 - cos^2theta))` ......[∵ (a + b)(a – b) = a2 – b2]
= `sintheta costheta xx 2/(sin^2theta)` .....`[(because sin^2theta + cos^2theta = 1),(therefore 1 - cos^2theta = sin^2theta)]`
= `2 xx (costheta)/(sintheta)`
= 2cot θ
= उजवी बाजू
∴ `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
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संबंधित प्रश्न
`(sin^2θ)/(cosθ) + cosθ = secθ`
cos2θ(1 + tan2θ) = 1
`1/(secθ - tanθ)` = secθ + tanθ
जर tanθ + `1/tanθ` = 2 तर दाखवा की `tan^2θ + 1/tan^2θ` = 2
sinθ × cosecθ = किती?
sec θ(1 - sin θ) (sec θ + tan θ) = 1
sec2θ – cos2θ = tan2θ + sin2θ हे सिद्ध करा.
`"cot A"/(1 - tan "A") + "tan A"/(1 - cot"A")` = 1 + tan A + cot A = sec A . cosec A + 1 हे सिद्ध करा.
(1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B हे सिद्ध करा.
θ चे निरसन करा:
जर x = r cosθ आणि y = r sinθ
