Question

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

Answer 1

@Mertsj

Answer 2

find the hypotenuse via pythagoras, or in your head, get \(\sqrt{2^2+1^2}=\sqrt{5}\)

Answer 3

that tells you
\[\cos(\theta)=-\frac{1}{\sqrt{5}}\]

Answer 4

then use the formula
\[\cos(2\theta)=2\cos^2(\theta)-1\] to finish the problem

Answer 5

thanks @satellite73

Answer 6

@edualvarez14 if you don't know why cos = -(.....) , just speak out, ok?
and it needs some more steps to get the final answer, do if you can.