Simplifying Trigonometric Functions

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Math › Simplifying Trigonometric Functions

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Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

$\frac{1+x}{2}$

$\frac{1-x}{2}$

$\frac{x}{2}$

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$