Question

Given tanTHETA = -2 and pi/2 < THETA < pi; find cos2THETA.

A: -4/3
B: -4/5
C: 3/4
D: -3/5

Answer 1

D)
`-(3)/(5)`

Explanation:

Given

`tan\theta=-2,\:(\pi)/(2)<\theta<\pi\\cos(2\theta)=?`

Use identities

`cos(2\theta)=(1-tan^2\theta)/(1+tan^2\theta)\\\\cos(2\theta)=(1-(-2)^2)/(1+(-2)^2)\\\\cos(2\theta)=(1-4)/(1+4)\\ \\cos(2\theta)=-(3)/(5)`