Question

Given: sin = 4/5 and cos x = -5/13 ; evaluate the following expression. Cos 2x

Answer 1

For every possible angle $x$, the fundamental law of trigonometric states that

$\sin^2(x)+\cos^2(x) = 1$

In your case, the inputs you provided would lead to

$\dfrac{16}{25}+\dfrac{25}{169} = \dfrac{3329}{4225} \approx 0.8 \neq 1$

So, it is not possible that, for a certain angle x, we have

$\sin(x) = \dfrac{4}{5},\quad \cos(x) = -\dfrac{5}{13}$