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

From the Figure Find the Value of Sinθ.

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प्रश्न

From the figure find the value of sinθ.

बेरीज
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उत्तर

`sinθ = ("AB")/("AC")`

`sinθ = 3/5`

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2018-2019 (March) Balbharati Model Question Paper Set 1

संबंधित प्रश्‍न

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

`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`

 


Prove the following trigonometric identities.

sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1


Prove the following trigonometric identities.

`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`


if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2  = 2`


Prove the following identities:

`cosA/(1 - sinA) = sec A + tan A`


` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`


If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`


If tan A =` 5/12` ,  find the value of (sin A+ cos A) sec A.


Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ


If sin θ − cos θ = 0 then the value of sin4θ + cos4θ


Prove the following identity :

`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ` 


Prove the following identity : 

`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`


Prove the following identity : 

`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`


sec2θ – tan2θ = ?


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`


If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ.


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


Prove that `(sin θ + "cosec"  θ)/(sin θ) = 2 + cot^2θ`.


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.


Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`


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