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प्रश्न
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
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उत्तर
`(1 - cos^2θ)sec^2θ = tan^2θ`
Consider L.H.S = `sin^2θ1/cos^2θ`
= `tan^2θ` = RHS
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संबंधित प्रश्न
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
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`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
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`1 - sin^2A/(1 + cosA) = cosA`
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x = 3 cosec θ + 4 cot θ
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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`
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
