मराठी

If `Sec Theta = X ,"Write the Value of Tan" Theta`. - Mathematics

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प्रश्न

If `sec theta = x ,"write the value of tan"  theta`.

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उत्तर

As , `tan^2 theta = sec^2 theta -1 `

So, `tan theta = sqrt( sec^2 theta -1 ) = sqrt( x^2 -1)`

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पाठ 8: Trigonometric Identities - Exercises 3

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आर. एस. अग्रवाल Mathematics [English] Class 10
पाठ 8 Trigonometric Identities
Exercises 3 | Q 40

संबंधित प्रश्‍न

If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`


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

`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`


Prove the following trigonometric identities.

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


Prove the following trigonometric identities.

`tan A/(1 + tan^2  A)^2 + cot A/((1 + cot^2 A)) = sin A  cos A`


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


cosec4θ − cosec2θ = cot4θ + cot2θ


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


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


If `secθ = 25/7 ` then find tanθ.


Prove the following identity : 

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


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`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`


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`sin((A + B)/2) = cos"C/2`


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


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


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


Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.


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


If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` 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`


Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.


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