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

If Sin θ = 1 2 , Then Find the Value of θ. - Geometry Mathematics 2

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प्रश्न

If sin θ = `1/2`, then find the value of θ. 

बेरीज
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उत्तर

sin θ = `1/2`

`sin 30^circ = 1/2`  ................ [using trignometric table]

∴ θ = 30°

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2018-2019 (July) Set 1

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संबंधित प्रश्‍न

If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1


Prove that:

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


`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`


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


Write the value of `4 tan^2 theta  - 4/ cos^2 theta`


Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\] 


Prove the following identity :

`cos^4A - sin^4A = 2cos^2A - 1`


Prove the following identity : 

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


Prove the following identity : 

`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`


Without using trigonometric identity , show that :

`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`


If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`


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


Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.


Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.


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


a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to


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

Activity:

`square` = 1 + tan2θ    ......[Fundamental trigonometric identity]

`square` – tan2θ = 1

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

`sqrt(3)*(sectheta - tan theta)` = 1

(sec θ – tan θ) = `square`


Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B


Prove the following:

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


Prove the following:

`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A


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