Advertisements
Advertisements
प्रश्न
If sec θ + tan θ = `sqrt(3)`, complete the activity to find the value of sec θ – tan θ
Activity:
`square` = 1 + tan2θ ......[Fundamental trigonometric identity]
`square` – tan2θ = 1
(sec θ + tan θ) . (sec θ – tan θ) = `square`
`sqrt(3)*(sectheta - tan theta)` = 1
(sec θ – tan θ) = `square`
Advertisements
उत्तर
sec2θ = 1 + tan2θ ......[Fundamental trigonometric identity]
sec2θ – tan2θ = 1
(sec θ + tan θ) . (sec θ – tan θ) = 1
`sqrt(3)*(sectheta - tan theta)` = 1
(sec θ – tan θ) = `1/sqrt(3)`
APPEARS IN
संबंधित प्रश्न
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
cos4 A − sin4 A is equal to ______.
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Evaluate:
sin2 34° + sin2 56° + 2 tan 18° tan 72° – cot2 30°
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
If tan θ = `13/12`, then cot θ = ?
If cos A + cos2A = 1, then sin2A + sin4 A = ?
If sin A = `1/2`, then the value of sec A is ______.
