SOLUTION: prove that 2arccos(4/5)=arcsin 24/25

Question 476243: prove that 2arccos(4/5)=arcsin 24/25
Found 2 solutions by lwsshak3, ccs2011:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
prove that 2arccos(4/5)=arcsin 24/25
**
Using a calculator:
2arccos(4/5)=2*36.8699�=73.7398�
arcsin 24/25=73.7398�
Therefore, 2arccos(4/5)=arcsin 24/25
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
arccos(4/5) equals the angle which satisfies the equation:
arcsin(24/25) equals the angle which satisfies the equation:
So we are proving that
Lets use a trig property for double angles.

Substitute

Now assume is true and check if it works.

Now use a trig identity:

It works
Therefore is equivalent to .
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