# Thread: Why the equation sin^-1(x)= cos^-1(2) cannot have a solution?

1. ## Why the equation sin^-1(x)= cos^-1(2) cannot have a solution?

Why the equation $\displaystyle sin^-1(x)= cos^-1(2)$ cannot have a solution?

(sin expontial -1) x = (cos exponential -1)2

2. Originally Posted by darkmoon123
Why the equation $\displaystyle sin^-1(x)= cos^-1(2)$ cannot have a solution?

(sin expontial -1) x = (cos exponential -1)2
$\displaystyle \cos^{-1}(2)$ does not have a real value.

3. Originally Posted by darkmoon123
Why the equation $\displaystyle sin^-1(x)= cos^-1(2)$ cannot have a solution?
The cosine outputs values only between -1 and +1. The inverse-cosine function can take inputs only between -1 and +1.

As such, the right-hand side of your equation is without mathematical meaning, which makes the entire equation nonsensical, and thus unsolveable.