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

If sec θ = 12, what will be the value of cos θ? - Geometry Mathematics 2

Advertisements
Advertisements

प्रश्न

If sec θ = `1/2`, what will be the value of cos θ?

पर्याय

  • 2

  • 1

  • 3

  • 5

MCQ
Advertisements

उत्तर

2

Explanation:

Given: sec θ = `1/2`

Since, sec θ = `1/cosθ`

∴ `1/2 =  1/cosθ`

⇒ cos θ = 2

Thus, the value of cos θ is 2.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2025-2026 (March) Model set 1 by shaalaa.com

संबंधित प्रश्‍न

State whether the following are true or false. Justify your answer.

sec A = `12/5` for some value of angle A.


If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`


If `sec θ = 13/5`, show that `(2 sin θ - 3 cos θ)/(4 sin θ - 9 cos θ) = 3`.


If `cot theta = 1/sqrt3` show that  `(1 - cos^2 theta)/(2 - sin^2  theta) = 3/5`


if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`


Evaluate the Following

`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`


The value of sin² 30° – cos² 30° is ______.


If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.


The value of the expression `[(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ]` is ______.


Prove the following:

If tan A = `3/4`, then sinA cosA = `12/25`


If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.


A ladder rests against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p so that its upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that `p/q = (cos β - cos α)/(sin α - sin β)`


Prove that: cot θ + tan θ = cosec θ·sec θ

Proof: L.H.S. = cot θ + tan θ

= `square/square + square/square`  ......`[∵ cot θ = square/square, tan θ = square/square]`

= `(square + square)/(square xx square)`  .....`[∵ square + square = 1]`

= `1/(square xx square)`

= `1/square xx 1/square`

= cosec θ·sec θ  ......`[∵ "cosec"  θ = 1/square, sec θ = 1/square]`

= R.H.S.

∴ L.H.S. = R.H.S.

∴ cot θ + tan θ = cosec·sec θ


`sqrt(3)` cos2A + `sqrt(3)` sin2A is equal to ______.


The maximum value of the expression 5cosα + 12sinα – 8 is equal to ______.


If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.


If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.


Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.


In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×