Question

Given tan of theta = -2 and pi/2; find cos(2theta)

Answer 1

[D] cos2θ = - 3/5

Answer 2

Given tan of theta = -2 and pi/2; find cos(2theta)
The identity of cos (2 theta)=
`cos(2\theta )=(1-tan^2\theta )/(1+tan^2\theta )`
Given tan of theta = -2 and pi/2.
So, let's plug in tan theta= -2

`cos(2\theta)= (1-(-2)^2)/(1+(-2)^2)`
=
`(1-4)/(1+4)` (Squaring)
=
`(-3)/(5)` (simplifying)
So, cos ( 2 theta) = -3/5.
Now we can plug in tan theta = π/2

`cos(2\theta)= (1-(π/2)^2)/(1+(π/2)^2)`
=
`(1-pi^2/4)/(1+pi^2/4)` (Squaring)
=
`(4-pi^2)/(4+pi^2)` Simplifying
So, cos ( 2 theta)= -3/5 and (4-pi^2)/(4+pi^2)