हिंदी

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

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प्रश्न

From the figure find the value of sinθ.

योग
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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:

`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`

`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`

`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`


Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`


 
 

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

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

[Hint : Simplify LHS and RHS separately.]

 
 

Prove the following trigonometric identities.

(sec2 θ − 1) (cosec2 θ − 1) = 1


Prove the following trigonometric identities.

sin2 A cot2 A + cos2 A tan2 A = 1


Prove the following trigonometric identities.

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


Prove the following trigonometric identities.

`(cot A + tan B)/(cot B + tan A) = cot A tan B`


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


Prove that:

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


`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec  theta)`


Show that none of the following is an identity:

`tan^2 theta + sin theta = cos^2 theta`


If `sin theta = x , " write the value of cot "theta .`


If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ. 


Prove the following identity : 

`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`


Without using trigonometric identity , show that :

`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`


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


If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.


Prove that sec2θ – cos2θ = tan2θ + sin2θ


If cos A = `(2sqrt("m"))/("m" + 1)`, then prove that cosec A = `("m" + 1)/("m" - 1)`


If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.


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