SOLUTION: Write the trigonometric expression as an algebraic expression. sin(arcsin x + arccos x)

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Question 1038722: Write the trigonometric expression as an algebraic expression.
sin(arcsin x + arccos x)
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write the trigonometric expression as an algebraic expression.
sin(arcsin x + arccos x)
--------------
arcsin + arcos of any angle = 90 degs or pi/2 radians
sin(90) = 1

Answer by ikleyn(52765) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write the trigonometric expression as an algebraic expression.
sin(arcsin x + arccos x)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Apply the formula for  sin%28alpha%2Bbeta%29.  It is

sin%28alpha%2Bbeta%29 = sin%28alpha%29%2Acos%28beta%29+%2B+cos%28alpha%29%2Asin%28beta%29.


Now,  sin%28arcsin%28x%29%29 = x  and  cos%28arcsin%28x%29%29 = sqrt%281-x%5E2%29. 

Therefore,

sin%28arcsin%28x%29+%2B+arccos%28x%29%29 = x%2Asqrt%281-x%5E2%29+%2B+sqrt%281-x%5E2%29%2Ax = 2x%2Asqrt%281-x%5E2%29.

Previous solution was wrong.