Find the maximum angle X in the range 0^{\circ} \leq

Write the trigonometric expression ${\displaystyle \cos ({\sin }^{-1}x-{\cos }^{-1}y)}$ as an algebraic expression (that is, without any trigonometric functions). Assume that x and y are positive and in the domain of the given inverse trigonometric function.

How do you find the exact value of ${\displaystyle {\cos }^{-1}0}$

Find the value of sin60.

$\sin \theta =\sqrt{\frac{2}{4}}$

Why does ${\displaystyle \sec \left(\frac{\pi }{4}\right)=\sqrt{2}}$?

Find the exact value of ${\displaystyle \frac{\pi }{6}}$

Given that ${\displaystyle f\left(x\right)=\cos x}$, show that ${\displaystyle \frac{f(x+h)-f\left(x\right)}{h}=\cos x\left(\frac{\text{cosh}-1}{h}\right)+\sin x\left(\frac{\text{sinh}}{h}\right)}$