SOLUTION: Hi, I was wondering if you could help me with the steps involved in determining all the exact solutions of sin^-1(x)=cos^-1(x) preferably without using the identity cos^-1(x

Question 854551: Hi, I was wondering if you could help me with the steps involved in determining all the exact solutions of
sin^-1(x)=cos^-1(x)
preferably without using the identity cos^-1(x) = pi/2 - sin^-1(x) unless you could explain why that identity is true
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
could help me with the steps involved in determining all the exact solutions of
sin^-1(x)=cos^-1(x)
----
Take the sin of both sides to get:
x = sin(arccos(x))
----
If the cos = x/1 the sin is sqrt(1-x^2)/1
---
So, x = sqrt(1-x^2)/1
------
x^2 = 1-x^2
2x^2 = 1
x = 1/sqrt(2)
And the angle whose sin is 1/sqrt(2) = 45 degrees or 135 degrees
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Cheers,
Stan H.
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