मराठी
महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

If sec θ = 257, then find the value of tan θ. - Geometry Mathematics 2

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

∵ 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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) Set 1

APPEARS IN

संबंधित प्रश्‍न

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.


if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`


Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2


Prove the following trigonometric identity.

`cos^2 A + 1/(1 + cot^2 A) = 1`


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+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`


Prove that:

2 sin2 A + cos4 A = 1 + sin4


Prove the following identities:

`cosA/(1 + sinA) + tanA = secA`


What is the value of (1 + cot2 θ) sin2 θ?


(sec A + tan A) (1 − sin A) = ______.


Prove the following identity : 

`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`


Prove that:

`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`


If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.


Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.


If x = h + a cos θ, y = k + b sin θ. 
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.


Prove the following identities.

cot θ + tan θ = sec θ cosec θ


Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0


To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.

Activity:

L.H.S = `square`

= `square/sintheta + sintheta/costheta`

= `(cos^2theta + sin^2theta)/square`

= `1/(sintheta*costheta)`     ......`[cos^2theta + sin^2theta = square]`

= `1/sintheta xx 1/square`

= `square`

= R.H.S


Prove that sin4A – cos4A = 1 – 2cos2A


Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos  (α - β)/2` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×