Inverse trignometric functions

Can someone show me how:

cos^-1 (x)= cos (x)

can be simplified to:

cos(x)=x

where did you see this?

There's a question in my ocr text book.

There's a question in my ocr text book.

p110 q6. The equation at the top is suppose to simplify to cos(X)=x according to the answer in the back of the book.

Can someone show me how:

cos^-1 (x)= cos (x)

can be simplified to:

cos(x)=x

Unfortunately I do not own this textbook.
Maybe another member does

If we have a function $f(x)$, the inverse function $f^{-1}x$ is (geometrically speaking) a reflection of the function $f(x)$ in the line $y=x$. This means that the function $f(x)$ will intersect the function $f^{-1}x$ on the line $y=x$

In this case, we have that $f(x) = \cos x$, this can be seen here:



Does this then enable you to see why your result is true. Since we have that $f(x) = \cos x$, then $f^{-1}x = \cos^{-1}x$, the solutions of $\cos^{-1} x= \cos x$ will be found on the line $y=x$, so either $cos x = x$ or tex]cos^{-1}x = x

Unfortunately my phone is out of battery at the moment. But the question was solving cosx^-1=cos x graphically and finding a simpler root equation.