Advertisements
Advertisements
प्रश्न
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
उत्तर
Given:` secθ+tanθ=x`
We know that,
`Sec^2θ-tan^2θ=1`
Therefore,
`sec^2 θ-tan^2θ=1`
⇒` (Secθ+tan θ) (Secθ-tan θ)=1`
⇒` x (secθ-tan θ )=1`
⇒ `(sec θ-tan θ)=1/x`
Hence, `sec θ-tan θ=1/4`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
Prove the following trigonometric identities.
`tan A/(1 + tan^2 A)^2 + cot A/((1 + cot^2 A)) = sin A cos A`
If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
Prove the following identity :
`tan^2A - sin^2A = tan^2A.sin^2A`
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
Without using trigonometric identity , show that :
`sin(50^circ + θ) - cos(40^circ - θ) = 0`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
