How many solutions does 2 (\sin^{-1}x)^2 -5\sin^{-1}x+2=0 have?

abiejose55d

abiejose55d

Answered question

2022-04-20

How many solutions does 2(sin1x)25sin1x+2=0 have?

Answer & Explanation

Narissiyks

Narissiyks

Beginner2022-04-21Added 7 answers

You have to reject x=sin2 as arcsin x is defined on [-1, 1] and takes values in [π2,π2] by definition. As 2 doesn’t belong to the last interval, this solution has to be rejected.
Draidayerabauu

Draidayerabauu

Beginner2022-04-22Added 9 answers

The (real-valued) arcsine returns a number in [π2,π2]. In particular arcsinsin2 is not 2, but π2, so it doesn't work.

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