cosx = 2tanx Find the numberical value of cos^2x.
K Kushballo7 New member Joined Oct 20, 2005 Messages 17 Nov 6, 2005 #1 cosx = 2tanx Find the numberical value of cos^2x.
U Unco Senior Member Joined Jul 21, 2005 Messages 1,134 Nov 6, 2005 #2 G'day, One way: Rewrite 2tanx as 2sinxcosx\displaystyle \frac{2\sin{x}}{\cos{x}}cosx2sinx Multiply through by cosx. Rewrite cos2x\displaystyle \cos^2{x}cos2x as 1−sin2x\displaystyle 1 - \sin^2{x}1−sin2x. Solve the quadratic -you may find it easier to let sinx = t, and solve for t using the quadratic formula, then relate back to x. Then get (cosx)^2 from there.
G'day, One way: Rewrite 2tanx as 2sinxcosx\displaystyle \frac{2\sin{x}}{\cos{x}}cosx2sinx Multiply through by cosx. Rewrite cos2x\displaystyle \cos^2{x}cos2x as 1−sin2x\displaystyle 1 - \sin^2{x}1−sin2x. Solve the quadratic -you may find it easier to let sinx = t, and solve for t using the quadratic formula, then relate back to x. Then get (cosx)^2 from there.
