SOLUTION: Find sin x/2, if tan (x) = 2 and 0<x<pi/2. The answer in the back of the books is {{{sqrt(50-10sqrt(5))/10}}}. I'm not getting anywhere near it!

Algebra ->  Trigonometry-basics -> SOLUTION: Find sin x/2, if tan (x) = 2 and 0<x<pi/2. The answer in the back of the books is {{{sqrt(50-10sqrt(5))/10}}}. I'm not getting anywhere near it!      Log On


   

Question 1053275: Find sin x/2, if tan (x) = 2 and 0 The answer in the back of the books is sqrt%2850-10sqrt%285%29%29%2F10.
I'm not getting anywhere near it!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+sin%28x%29+%2F+cos%28x%29+=+2%2F1+
+sin%28x%29+=+2%2Acos%28x%29+
+sin%28x%29%5E2+%2B+cos%28x%29%5E2+=+1+
+4%2Acos%28x%29%5E2+%2B+cos%28x%29%5E2+=+1+
+cos%28x%29%5E2+=+1%2F5+
+cos%28x%29+=+1%2Fsqrt%285%29+
------------------------
The formula is:
+sin%28x%2F2+%29+=+sqrt%28+%28+1+-+cos%28x%29+%29+%2F+2+%29+
+sin%28+x%2F2+%29+=+sqrt%28+%28+1+-+1%2Fsqrt%285%29+%29+%2F+2+%29+
+sin%28+x%2F2+%29+=+sqrt%28+%28+100%2F100+-+100%2F%28100%2Asqrt%285%29+%29%29+%2F+2+%29+
+sin%28+x%2F2+%29+=+%28+1%2F10+%29%2Asqrt%28+%28+100+-+100%2Fsqrt%285%29+%29%2F+2+%29+

+sin%28+x%2F2+%29+=+%28+1%2F10+%29%2Asqrt%28+%28+50+-+10%2Asqrt%285%29+%29+%29+
It's a real contortion to end up with this, and
I don't see any advantage to doing it, but it
does seem you can get there.