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

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

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

arccos (x) - arcsin (x) = arccos (\frac{3}{2})

x = \frac{1}{2}

Solution steps

arccos (x) - arcsin (x) = arccos (\frac{3}{2})

a = b \Rightarrow cos (a) = cos (b)

cos (arccos (x) - arcsin (x)) = cos (arccos (\frac{3}{2}))

Use the following identity:

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

cos (arccos (x)) cos (arcsin (x)) + sin (arccos (x)) sin (arcsin (x)) = cos (arccos (\frac{3}{2}))

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}

Use the following identity:

sin (arcsin (x)) = x

x 1 - x^{2} + 1 - x^{2} x = \frac{3}{2}

Solve

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

x = \frac{1}{2}, x = \frac{3}{2}

Verify solutions by plugging them into the original equation

x = \frac{1}{2}

- 5 tan (θ) - 12 = tan (θ) - 8

\frac{1}{4} sin (4 t) = 0

csc (x) + 2 = 0, (0, 2 π)

2 cos (4 x) = 2 cos^{2} (2 x) - sin (2 x) - 1

x, sin (x - 4 0^{\circ}) = cos (y - 2 0^{\circ})

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