How do you solve $sqrtsinx=2sinx-1$ ?

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Answer 1 · 2016-10-14T19:05:31

Square both sides:

$(sqrt(sinx))^2 = (2sinx - 1)^2$

$sinx = 4sin^2x - 4sinx + 1$

$0 = 4sin^2x - 5sinx + 1$

$0 = 4sin^2x - 4sinx - sinx + 1$

$0 = 4sinx(sinx - 1) - (sinx - 1)$

$0 = (4sinx - 1)(sinx - 1)$

$sinx = 1/4 and sinx = 1$

$x = arcsin(1/4) and x = pi/2$

Hopefully this helps!

How do you solve sqrtsinx=2sinx-1sqrtsinx=2sinx-1?