Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
Advertisements
उत्तर
`(1 - sin^2 A/cos^2 A)/(cos^2 A/sin^2 A -1) = ((cos^2 A - sin^2 A)/cos^2 A)/((cos^2 A - sin^2 A)/sin^2 A`
`= (sin^2 A)/cos^2 A`
`= tan^2 A`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Show that : tan 10° tan 15° tan 75° tan 80° = 1
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Choose the correct alternative:
1 + tan2 θ = ?
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
Prove that `(1 + sin B)/(cos B) + (cos B)/(1 + sin B) = 2 sec B`.
Prove that `sec^2A - "cosec"^2A = (2sin^2A - 1)/(sin^2A *cos^2A)`.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
