arcsin x + arcsin 2x = pi/2

[Michael_Light]

1. The problem statement, all variables and given/known data

sin -1x + sin -12x = ∏/2



2. Relevant equations



3. The attempt at a solution

My question is, is it possible for x to be a negative value? Since ∏/2 is positive. Or I should think that x can be negative because -(3∏)/2 = ∏/2?

Please enlighten me...
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[SammyS]

sin-1(x) has the same sign as x , so the answer to your question is "No, that's not possible."

[ehild]

-3pi/2 is not equal to pi/2, but the angle -3pi/2 is equivalent to the angle pi/2.:smile:

The range of the inverse sine function is [-pi/2,pi/2]. -3pi/2 is outside of the range.

Hints to solve the problem:

sin(sin-1(x))=x.

sin(pi/2-α)=cosα.

What is cos(sin-1(x))?

ehild