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प्रश्न
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
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उत्तर
L.H.S. = `((1 + tan^2A)cotA)/(cosec^2A)`
= `(sec^2A cotA)/(cosec^2A` ...(∵ sec2 A = 1 + tan2 A)
= `(1/(cos^2A) xx (cosA)/(sinA))/(1/(sin^2A))`
= `(1/(cosA sinA))/(1/(sin^2A))`
= `sinA/cosA`
= tan A = R.H.S.
संबंधित प्रश्न
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
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`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`
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If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.
Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
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