Home
Class 11
MATHS
If 2 cos alpha = x + 1/x , 2 cos beta =...

If ` 2 cos alpha = x + 1/x , 2 cos beta = y + 1/ y , 2 cos gamma = z + 1/z` then `xyz + 1/(xyz)` =

Text Solution

Verified by Experts

` 2 cos alpha = x + 1/x `
`2 x cos alpha = x^2 + 1`
`x^2 - 2x cos alpha - 1= 0`
`x = -((-2cos alpha) +- sqrt(4 cos^2 alpha- 4))/2`
`= cos alpha +- i sin alpha`
`= e^(i alpha) or e^(-i alpha)`
`x = e^(i alpha) or e^(-i alpha)`
`y = e^(i beta) or e^(- i beta)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that x^(m) y^(n) + (1)/(x^(m)y^(n)) = 2 cos (m alpha + n beta)

IF alpha , beta and gamma are angles such that tan alpha + tan beta + tan gamma = tan alpha tan beta tan gamma and x= cos alpha + i sin alpha , y = cos beta + i sin beta and z= cos gamma + i sin gamma , then xyz =

If x+1/x=2cos alpha,y+1/y=2cos beta, then xy+(1)/(xy)=

If cos alpha =1/2(x+1/x),cos beta=1/2(y+1/y) then evaluate cos(alpha-beta)

If alpha, beta and gamma are angle such that tan alpha + tan beta+tan gamma= tan alpha tan beta tan gammaand x=cos alpha + I sin alpha, y=cos beta+ I sin beta and z= cos gamma+ I sin gamma, then the value of xyz is -

If x=r cos alpha cos beta cos gamma , y= cos alpha cos beta sin gamma , z= r sin alpha cos beta , mu = r sin beta " then " x^(2)+y^(2) + z^(2)+mu^(2)=

If (x) / (a) cos alpha + (y) / (b) sin alpha = 1, (x) / (a) cos beta + (y) / (b) sin beta = 1 and (cos alpha cos beta) / (a ^ (2)) + (without alpha without beta) / (b ^ (2)) = 0 then

Let x+1/x=2cos alpha, y+1/y=2cos beta z+1/z=2cosgamma."Show that"2 "cos"(alpha+beta+gamma)=xyz+1/(xyz)

If x=cos alpha+i sin alpha and y=cos beta+i sin beta,z=cos gamma+i sin gamma and if x+y+z=0 then prove that (1)/(x)+(1)/(y)+(1)/(z)=0

If alpha,beta and gamma are angles such that tan alpha+tan beta+tan gamma=tan alpha tan beta tan gamma and x=cos alpha+i sin alpha,y=cos beta+i sin beta and z=cos gamma+i sin gamma then the value of xyz is