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