Simplifying Trigonometric Functions - High School Math

Card 0 of 1

Question

Simplify the function below:

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

Answer

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:

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

Compare your answer with the correct one above

Tap the card to reveal the answer