рд╣рд┐рдВрджреА

`(1+ Cos Theta - Sin^2 Theta )/(Sin Theta (1+ Cos Theta))= Cot Theta` - Mathematics

Advertisements
Advertisements

рдкреНрд░рд╢реНрди

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

Advertisements

рдЙрддреНрддрд░

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

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

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

     =`(cos theta ( 1+ cos theta ))/ ( sin theta ( 1+ cos theta))`

     =`cos theta/ sin theta`

     = cot ЁЭЬГ
     = RHS
Hence, L.H.S. = R.H.S.

  

shaalaa.com
  рдХреНрдпрд╛ рдЗрд╕ рдкреНрд░рд╢реНрди рдпрд╛ рдЙрддреНрддрд░ рдореЗрдВ рдХреЛрдИ рддреНрд░реБрдЯрд┐ рд╣реИ?
рдЕрдзреНрдпрд╛рдп 8: Trigonometric Identities - Exercises 1

APPEARS IN

рдЖрд░.рдПрд╕. рдЕрдЧреНрд░рд╡рд╛рд▓ Mathematics [English] Class 10
рдЕрдзреНрдпрд╛рдп 8 Trigonometric Identities
Exercises 1 | Q 25

рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди

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


If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1


Prove the following trigonometric identities.

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


If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2


Prove the following identities:

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


Prove that:

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


Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`


If sec A + tan A = p, show that:

`sin A = (p^2 - 1)/(p^2 + 1)`


cosec4 θ − cosec2 θ = cot4 θ + cot2 θ


`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`


If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.


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


The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to 


Prove the following Identities :

`(cosecA)/(cotA+tanA)=cosA`


If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.


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


Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.


Prove the following identities.

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


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


If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.


Share
Notifications

Englishрд╣рд┐рдВрджреАрдорд░рд╛рдареА


      Forgot password?
Use app×