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प्रश्न
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
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उत्तर
`= 1/(cosectheta-cottheta)xx (cosectheta+cottheta)/(cosectheta+cottheta)-1/sintheta`
`= (cosectheta+cottheta)/(cosec^2theta-cot^2theta) - 1/sintheta`
`cosectheta+cottheta - 1/sintheta`
`1/sintheta+costheta/sintheta - 1/sintheta`
`1/sintheta+(costheta-1)/sinthetaxx(costheta+1)/(costheta+1)`
`1/sintheta+(cos^2theta-1)/((1+costheta)sintheta)`
`1/sintheta-(1-cos^2theta)/(sintheta(1+costheta))`
`1/sintheta - (sin2theta)/(sintheta(1+costheta))`
`1/sintheta-sintheta/(1+costheta)`
`1/sintheta - (sintheta/sintheta)/(1/sintheta+costheta/sintheta)`
`1/sintheta-1/(cosectheta+cottheta)`= RHS
संबंधित प्रश्न
Prove the following identities:
`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`
`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`
`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
