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प्रश्न
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
उत्तर
LHS = mn = (secθ + tanθ) (secθ - tanθ)
⇒ LHS = `sec^2θ - tan^2θ` [Because (a-b)(a+b) = a2 - b2]
⇒ LHS = 1 [Since `1 + tan^2θ = sec^2θ`]
Hence , mn = 1
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संबंधित प्रश्न
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
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`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
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(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
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`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
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Prove the following identities.
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`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`
