Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Advertisements
उत्तर
`sec^4A - sec^2A = 1/cos^4A - 1/cos^2A`
= `(1 - cos^2A)/cos^4A`
= `sin^2A/cos^4A` [∵ `sin^2A = 1 - cos^2A`]
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Prove that `(cosθ)/(1 + sinθ) = (1 - sinθ)/(cosθ)`.
