Question

Find the exact value by using a half-angle identity.
sine of seven pi divided by eight.
This is my answer below. Can someone please check it to see if I have the correct answer step by step.
sin (7π/8)=√1-cos(7π/4/2)
sin (7π/4)=√2/√2
sin Θ/2=±√1-cos (Θ)/2 =±√1-√2/2/2
+√2-√2/4=+√2-√2/2=2/√2-2

Answer 1

@ganeshie8

Answer 2

\[\large \sin \left(\dfrac{7\pi}{8}\right) = \sqrt{\dfrac{1-\cos(7\pi/4)}{2}}\]

Answer 3

cos(7pi/4) = cos(pi/4) = 1/sqrt(2)

Answer 4

\[\large \begin{align}\sin \left(\dfrac{7\pi}{8}\right) &= \sqrt{\dfrac{1-\cos(7\pi/4)}{2}}\\~\\&=\sqrt{\dfrac{1-1/\sqrt{2}}{2}}\\~\\&=\sqrt{\dfrac{\sqrt{2}-1}{2\sqrt{2}}}\\~\\&= \sqrt{\dfrac{2-\sqrt{2}}{4}}\\~\\&= \dfrac{\sqrt{2-\sqrt{2}}}{2}\end{align}\]

Answer 5

btw, your answer is also correct

Answer 6

Is that a different way to do it or is my process wrong?

Answer 7

yeah i see few mistakes in your work in last two lines now, but its hard to make sense of what you wrote without proper latex :O

Answer 8

Okay and thank you :)