Question

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

Answer 1

Answer:

[D]  cos2θ = - 3/5

Answer 2

Given tan of theta = -2 and pi/2; find cos(2theta)
The identity of cos (2 theta)= $cos(2\theta )=\frac{1-tan^2\theta }{1+tan^2\theta }$
Given tan of theta = -2 and pi/2.
So, let's plug in tan theta= -2
$cos(2\theta)= \frac{1-(-2)^2}{1+(-2)^2}$
=$\frac{1-4}{1+4}$ (Squaring)
=$\frac{-3}{5}$ (simplifying)
So, cos ( 2 theta) = -3/5.
Now we can plug in tan theta = π/2
$cos(2\theta)= \frac{1-(π/2)^2}{1+(π/2)^2}$
= $\frac{1-pi^2/4}{1+pi^2/4}$ (Squaring)
=$\frac{4-pi^2}{4+pi^2}$ Simplifying
So, cos ( 2 theta)= -3/5 and (4-pi^2)/(4+pi^2)