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

`(16)/(25)+(25)/(169) = (3329)/(4225) \approx 0.8 \\eq 1`

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

`\sin(x) = (4)/(5),\quad \cos(x) = -(5)/(13)`