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

Cos 45° = ? A) sin 45° B) sec 45° C) cot 45° D) tan 45°

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प्रश्न

cos 45° = ?

पर्याय

  • sin 45°

  • sec 45°

  • cot 45°

  • tan 45°

MCQ
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उत्तर

sin 45°

Explanation:

`cos 45^circ = 1/sqrt2`, `sin 45^circ = 1/sqrt(2)`

∴ cos 45° = sin 45°

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पाठ 6: Trigonometry - Exercise

संबंधित प्रश्‍न

Prove the following trigonometric identities.

`((1 + tan^2 theta)cot theta)/(cosec^2 theta)   = tan theta`


Prove the following trigonometric identities.

`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`


If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A


`sqrt((1-cos theta)/(1+cos theta)) = (cosec  theta - cot  theta)`


Prove the following identities:

`(sin theta + 1 - cos theta)/(cos theta - 1 + sin theta) = (1 + sin theta)/(cos theta)`


Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`


Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`


If `cosec  theta = 2x and cot theta = 2/x ," find the value of"  2 ( x^2 - 1/ (x^2))`


If `sec theta = x ,"write the value of tan"  theta`.


What is the value of \[6 \tan^2 \theta - \frac{6}{\cos^2 \theta}\]


Prove the following identity : 

`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`


Prove the following identity : 

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


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


Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A


Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A


If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.


If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.

Activity:

`square = 1 + tan^2θ`   ...[Fundamental trigonometric identity]

`square - tan^2θ = 1`

`(sec θ + tan θ) . (sec θ - tan θ) = square`

`sqrt(3)  . (sec θ - tan θ) = 1`

`(sec θ - tan θ) = square`


Prove that cot2θ – tan2θ = cosec2θ – sec2θ.


Prove that `(sin θ)/(sec θ + 1) + (sin θ)/(sec θ - 1) = 2 cot θ`.


Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)


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