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`Sqrt((1-cos Theta)/(1+Cos Theta)) = (Cosec Theta - Cot Theta)` - Mathematics

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

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LHS = `sqrt((1-cos theta)/(1+ cos theta))`

      =`sqrt(((1-cos theta))/((1+cos theta)) xx ((1- cos theta))/((1 - cos theta))`

      =`sqrt((1-cos theta)^2 / (1-cos^2 theta))`

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

     =`(1-cos theta)/sin theta`

     =`1/sin theta - cos theta/ sin theta`

     =(ЁЭСРЁЭСЬЁЭСаЁЭСТЁЭСР ЁЭЬГ − cot ЁЭЬГ)
      = RHS

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рдЕрдзреНрдпрд╛рдп 8: Trigonometric Identities - Exercises 1

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рдЖрд░.рдПрд╕. рдЕрдЧреНрд░рд╡рд╛рд▓ Mathematics [English] Class 10
рдЕрдзреНрдпрд╛рдп 8 Trigonometric Identities
Exercises 1 | Q 21.2

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


Prove the following trigonometric identities.

sec6θ = tan6θ + 3 tan2θ sec2θ + 1


Prove the following trigonometric identities.

if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1


Prove the following identities:

(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A


Prove the following identities:

`(sinAtanA)/(1 - cosA) = 1 + secA`


Prove the following identities:

(1 + cot A – cosec A)(1 + tan A + sec A) = 2


Prove the following identities:

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


`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`


`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`

 


Write the value of `(cot^2 theta -  1/(sin^2 theta))`. 


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


If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`


Prove the following identity : 

`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`


Prove the following identity : 

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


Prove the following identity : 

`sec^4A - sec^2A = sin^2A/cos^4A`


Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = cosec θ - cot θ`.


If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.


Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ


Prove the following:

(sin α + cos α)(tan α + cot α) = sec α + cosec α


tan θ × `sqrt(1 - sin^2 θ)` is equal to:


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