English
Maharashtra State BoardSSC (English Medium) 10th Standard

If sec θ = 257, then find the value of tan θ.

Advertisements
Advertisements

Question

If sec θ = `25/7`, then find the value of tan θ.

Sum
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`  

shaalaa.com
  Is there an error in this question or solution?
2018-2019 (March) Set 1

APPEARS IN

RELATED QUESTIONS

9 sec2 A − 9 tan2 A = ______.


Prove the following trigonometric identities.

tan2θ cos2θ = 1 − cos2θ


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`


Prove the following identities:

`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`


Prove the following identities:

sec4 A (1 – sin4 A) – 2 tan2 A = 1


Prove that:

cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A


`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`


The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to 


Prove the following identity :

cosecθ(1 + cosθ)(cosecθ - cotθ) = 1


If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that   `x^2 + y^2 + z^2 = r^2`


If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`


Without using trigonometric table , evaluate : 

`cosec49°cos41° + (tan31°)/(cot59°)`


Prove that  `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`


For ΔABC , prove that : 

`sin((A + B)/2) = cos"C/2`


Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.


Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2 "cosec"θ`


If 2sin2θ – cos2θ = 2, then find the value of θ.


Complete the following activity to prove:

cotθ + tanθ = cosecθ × secθ

Activity: L.H.S. = cotθ + tanθ

= `cosθ/sinθ + square/cosθ`

= `(square + sin^2theta)/(sinθ xx cosθ)`

= `1/(sinθ xx  cosθ)` ....... ∵ `square`

= `1/sinθ xx 1/cosθ`

= `square xx secθ`

∴ L.H.S. = R.H.S.


(1 + sin A)(1 – sin A) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×