Home
Class 12
MATHS
If x(1), x(2) , x(3) , x(4) are the roo...

If ` x_(1), x_(2) , x_(3) , x_(4)` are the roots of the equation `x^(4) - x^(3) sin 2 beta + x^(2) cos 2 beta - x cos beta - sin beta = 0 `
Then show :
` tan ^(-1) x_(1) + tan^(-1) x_(2) + tan^(-1) x_(3) + tan^(-1) x_(4) = pi/2 - beta`

A

`alpha`

B

`90^(@)- alpha`

C

`180^(@)- alpha`

D

`270^(@) - alpha`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exericse 2.1|14 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exericse 2.2|21 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exericse 2b|10 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|44 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|9 Videos

Similar Questions

Explore conceptually related problems

If x_1,x_2, x_3, x_4 are the roots of the equation x^4-x^3 sin2 beta+ x^2.cos2 beta-xcos beta-sin beta=0 , then tan^-1x_1+tan^-1x_2+tan^-1x_3+tan^-1x_4 is equal to

If x_1, x_2, x_3 and x_4 are the roots of the equations x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0, prove that tan^(-1)x_1+tan^(-1)x_2+tan^(-1)x_3+tan^(-1)x_4=(pi/2)-beta .

If tan theta_1,tantheta_2,tan theta_3,tan theta_4 are the roots of the equation x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0 then prove that tan(theta_1+theta_2+theta_3+theta_4)=cot beta

If tan theta_1,tantheta_2,tan theta_3,tan theta_4 are the roots of the equation x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0 then prove that tan(theta_1+theta_2+theta_3+theta_4)=cot beta

Let alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

If alpha and beta are the roots of the equation 2x^(2) - 3x + 4 = 0 , then alpha^(2) + beta^(2) = ____

If alpha , beta , gamma are the roots of the equation x^3 +4x^2 -5x +3=0 then sum (1)/( alpha^2 beta^2)=

If alpha,beta are the roots of the equation x^(2)+x+1=0 , find the value of alpha^(3)-beta^(3) .

Solve for x : tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4

Solve for x : tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4