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प्रश्न
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove the following:
`secA/(secA + 1) + secA/(secA - 1) = 2"cosec"^2A`
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उत्तर
L.H.S. = `secA/(secA + 1) + secA/(secA - 1)`
= `(sec^2A - secA + sec^2A + secA)/(sec^2A - 1`
= `(2sec^2A)/tan^2A` ...(∵ sec2 A – 1 = tan2 A)
= `(2/cos^2A)/(sin^2A/cos^2A)`
= `2/sin^2A`
= 2 cosec2 A = R.H.S.
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संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
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Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
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`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
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`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
If tan θ = `9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ......[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
