рдорд░рд╛рдареА

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

Advertisements
Advertisements

рдкреНрд░рд╢реНрди

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

Advertisements

рдЙрддреНрддрд░

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

shaalaa.com
  рдпрд╛ рдкреНрд░рд╢реНрдирд╛рдд рдХрд┐рдВрд╡рд╛ рдЙрддреНрддрд░рд╛рдд рдХрд╛рд╣реА рддреНрд░реБрдЯреА рдЖрд╣реЗ рдХрд╛?

рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди

 
 

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 that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2


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.

`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`


Prove that

`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`


Prove the following identities:

sec2A + cosec2A = sec2A . cosec2A


Prove that:

`cot^2A/(cosecA - 1) - 1 = cosecA`


Prove that:

(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A


Prove the following identities:

`sin theta/((cot theta + "cosec"  theta)) - sin theta/((cot theta - "cosec"  theta)) = 2`


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


Prove the following identity :

tanA+cotA=secAcosecA 


Prove the following identity :

`cosec^4A - cosec^2A = cot^4A + cot^2A`


Prove the following identity :

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


Prove the following identity :

`(cotA + tanB)/(cotB + tanA) = cotAtanB`


Prove the following identity :

`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`


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


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


If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to


Prove that `(tan(90 - θ) + cot(90 - θ))/("cosec"  θ) = sec θ`.


If 2sin2θ – cos2θ = 2, then find the value of θ.


Share
Notifications

Englishрд╣рд┐рдВрджреАрдорд░рд╛рдареА


      Forgot password?
Use app×