Solving for x in \sin^{-1}(2x) + \sin^{-1}(3x) = \frac{\pi}{4} I tried

Emmy Combs

Emmy Combs

Answered question

2022-01-26

Solving for x in sin1(2x)+sin1(3x)=π4
I tried solving by differentiating both sides, but I get x=0.
How do you solve it, purely using trigonometric techniques?

Answer & Explanation

Eleanor Shaffer

Eleanor Shaffer

Beginner2022-01-27Added 16 answers

Or this way using
cos(a+b)=cosacosbsinasinb
cosa=1sin2a
sin1(2x)+sin1(3x)=π4
14x219x26x2=22
(14x2)(19x2)=(22+6x2)2
12=(62+13)x2
The positive solution gives:
x=12(62+13)

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