Advertisements
Advertisements
Question
If sec θ = `25/7`, then find the value of tan θ.
Advertisements
Solution
∵ sec2θ – tan2θ = 1 ......[Identities]
`(25/7)^2 - ("tan" theta)^2 = 1`
`625/49 -1 = ("tan" theta)^2`
`(625 - 49)/49 = ("tan" theta)^2`
`576/49 = ("tan" theta)^2`
`"tan" theta = 24/7`
APPEARS IN
RELATED QUESTIONS
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.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
If 4 tanβ = 3, then `(4sinbeta-3cosbeta)/(4sinbeta+3cosbeta)=` ______.
