Advertisements
Advertisements
प्रश्न
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
उत्तर
L.H.S = `(cosec A - sin A)(secA - cosA)sec^2A`
`= (1/sinA - sinA)(1/cosA - cosA)(1/cos^2A)`
`= ((1 - sin^2A)/sin A)((1- cos^2A)/cos A)(1/(cos^2A))`
`= cos^2A/sinA . sin^2A/cos A . 1/cos^2A`
`= sinA/cosA`
= tan A
= R.H.S
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following trigonometric identities.
`tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta`
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
sin(45° + θ) – cos(45° – θ) is equal to ______.
