What is the general solution for arcsin(x)-arccos(x)=arcsin(3x-2) ?

The general solution for arcsin(x)-arccos(x)=arcsin(3x-2) is x=1,x= 1/2

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arcsin(x)-arccos(x)=arcsin(3x-2)

arcsin (x) - arccos (x) = arcsin (3 x - 2)

x = 1, x = \frac{1}{2}

Solution steps

arcsin (x) - arccos (x) = arcsin (3 x - 2)

a = b \Rightarrow sin (a) = sin (b)

sin (arcsin (x) - arccos (x)) = sin (arcsin (3 x - 2))

Use the following identity:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

sin (arcsin (x)) cos (arccos (x)) - cos (arcsin (x)) sin (arccos (x)) = sin (arcsin (3 x - 2))

Use the following identity:

sin (arcsin (x)) = x

Use the following identity:

cos (arccos (x)) = x

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

xx - 1 - x^{2} 1 - x^{2} = 3 x - 2

Solve

xx - 1 - x^{2} 1 - x^{2} = 3 x - 2 : x = 1, x = \frac{1}{2}

x = 1, x = \frac{1}{2}

Verify solutions by plugging them into the original equation

x = 1, x = \frac{1}{2}

cos (a) = - 0.6

15 arcsin (x) = 5 π

2 sin^{2} (x) - sin (x) = 0, 0 \leq x < 2 π

sin (x) = \frac{3}{7}

2 sin (θ) + 6 = - 3 + 6

What is the general solution for arcsin(x)-arccos(x)=arcsin(3x-2) ?
The general solution for arcsin(x)-arccos(x)=arcsin(3x-2) is x=1,x= 1/2