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

From the Figure Find the Value of Sinθ. - Geometry Mathematics 2

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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:

`sqrt((1+sinA)/(1-sinA)) = secA + tanA`


Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`


Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.


As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.


Prove the following trigonometric identities.

tan2 θ − sin2 θ = tan2 θ sin2 θ


Prove that:

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


Prove that:

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


Prove that

`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`


If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`


Write the value of tan10° tan 20° tan 70° tan 80° .


Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50°   cosec 40 °`


What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]


\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to 

 

 


Prove the following identity : 

`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`


Choose the correct alternative:

1 + tan2 θ = ?


Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.


If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`


If tan θ = `9/40`, complete the activity to find the value of sec θ.

Activity:

sec2θ = 1 + `square`     ......[Fundamental trigonometric identity]

sec2θ = 1 + `square^2`

sec2θ = 1 + `square` 

sec θ = `square` 


Prove that `"cot A"/(1 - cot"A") + "tan A"/(1 - tan "A")` = – 1


Prove the following:

`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ


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