Simplify each expression.
5 c) 1-2sin^2 3π/8
I got 1-2sin^2 67.5
Cos2Θ= 1-2sin^2 67.5
I dont know exactly what to do from there...
Leave it in terms of $\displaystyle \pi$ otherwise you will never solve it
$\displaystyle 1-2sin^2 \left(\frac{3\pi}{8}\right) = cos \left(\frac{3\pi}{4}\right)$ (because $\displaystyle 2 \times \frac{3}{8} = \frac{3}{4}$)
$\displaystyle cos \left(\frac{3\pi}{4}\right) = cos \left(\pi - \frac{\pi}{4}\right)$
To solve use the angle difference formula: $\displaystyle cos(A-B) = cosAcosB+sinAsinB$
Spoiler:
I used the double angle formula for cos:
$\displaystyle 1-2sin^2 \theta = cos(2 \theta)$
Therefore $\displaystyle 1-2sin^2 \left(\frac{3\pi}{8}\right) = cos \left(2 \cdot \frac{3\pi}{8}\right)$
$\displaystyle \frac{3\pi}{4}$ comes from simplifying the cos term
$\displaystyle 2 \times \frac{3\pi}{8} = \frac{6\pi}{8} = \frac{3\pi}{4}$
The 3 is turned into a 4-1. If you imagine $\displaystyle \pi = \frac{4\pi}{4}$ then we see that
$\displaystyle \frac{4\pi}{4}-\frac{\pi}{4} = \frac{3\pi}{4}$
I used $\displaystyle \pi $and $\displaystyle \frac{\pi}{4}$ because their exact values are known