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प्रश्न
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
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उत्तर
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
`cot^2A - 2cotA cosecA + cosec^2x = (1 - cosA)/(1 + cosA)`
`(cos^2A)/(sin^2A) - (2cosA)/(sin^2A) + 1/(sin^2A) = (1 - cosA)/(1 + cosA)`
`(cos^2A - 2cosA + 1)/(sin^2A) = (1 - cosA)/(1 + cosA)`
`(cos^2A - 2cosA + 1)/(1 - cos^2A) = (1 - cosA)/(1 + cosA)`
`((1 - cosA)(1 - cosA))/((1 + cosA)(1 - cosA)) = (1 - cosA)/(1 + cosA)`
`(1 - cosA)/(1 + cosA) = (1 - cosA)/(1 + cosA)`
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following identities:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
If `tan A = 5/12`, find the value of (sin A + cos A) sec A.
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
