Is it possible for x to be negative in the equation arcsin x + arcsin 2x = pi/2?

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The discussion centers on whether x can be negative in the equation arcsin x + arcsin 2x = π/2. It is clarified that since arcsin(x) has the same sign as x, x cannot be negative because π/2 is positive. The range of the inverse sine function is limited to [-π/2, π/2], making -3π/2 an invalid angle in this context. Hints are provided to help solve the equation, emphasizing the relationship between sine and cosine functions. Ultimately, x must be non-negative for the equation to hold true.
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Homework Statement



sin -1x + sin -12x = ∏/2



Homework Equations





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

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