Advertisements
Advertisements
प्रश्न
If sec θ = `25/7`, find the value of tan θ.
Solution:
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^square`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
= `square/49`
∴ tan θ = `square/7` ........(by taking square roots)
Advertisements
उत्तर
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^2`
∴ tan2 θ = `625/49 - 1`
= `(625 - 49)/49`
= `576/49`
∴ tan θ = `24/7` ........(by taking square roots)
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
Prove that:
tan (55° + x) = cot (35° – x)
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
Prove that `(tan(90 - θ) + cot(90 - θ))/("cosec" θ) = sec θ`.
Prove that cosec θ – cot θ = `(sin θ)/(1 + cos θ)`.
If cos A = `(2sqrt(m))/(m + 1)`, then prove that cosec A = `(m + 1)/(m - 1)`.
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
