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प्रश्न
Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.
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उत्तर
LHS = sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ )
= sec θ. sec θ - tan θ. tan θ
= sec2θ - tan2θ
= 1
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
Prove that cosec θ – cot θ = `(sin θ)/(1 + cos θ)`.
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
Eliminate θ if x = r cosθ and y = r sinθ.
