First, you have to know the double angle formula:
sin 2A = 2 sin A cos A
cos 2A = cos² A − sin² A = 2 cos² A − 1 = 1 − 2 sin² A
tan 2A<span> = 2 tan </span>A<span> / (1 − tan² </span>A)
Next, find the other leg: 17^2-15^=64, √64 is 8, so the unknown leg length is 8.
sinα=15/17, cosα=8/17, tanα=15/8
sinβ=8/17, cosβ15/17, tanβ=8/15
Plug these values in the above formula, you'll have your answers.
For the half angles, know the half-angle formula:
sin(B/2) = ± √<span>(1 − cos B)/2</span>
cos(B/2) = ± √<span>(1 + cos B)/2</span>
tan(B/2) = (1 − cos B) / sin B<span> = sin </span>B<span> / (1 + cos </span>B)
refer to this website for details:
<span>https://brownmath.com/twt/double.htm
</span>
For the power reduction formula, please search for it. I tried to copy and paste here, but it wouldn't paste.
for number 4, factor the quadratic equation into (cscx-8)(cscx+1)=0
cscx=8 or cscx=-1
You may not have the csc button on your calculator. Recall that csc is 1/sin, so sinx=1/8 or sinx=-1, so x is either 7.18 or 270 degrees
