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

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

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arccos((sqrt(3))/2)+arcsin(3x)= pi/2

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

x = \frac{1}{2 3}

Solution steps

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

arccos (\frac{3}{2}) = \frac{π}{6}

\frac{π}{6} + arcsin (3 x) = \frac{π}{2}

Move

\frac{π}{6}

to the right side

arcsin (3 x) = \frac{π}{3}

Apply trig inverse properties

3 x = \frac{3}{2}

Solve

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

x = \frac{1}{2 3}

2 sin (x) = 5 cos (x), 0^{\circ} \leq x < 36 0^{\circ}

cos (x) = \frac{1 - 2}{26}

4 cos (2 x) - 2 sin (2 x) = 0

cos (2 x) sin (x) + sin (x) = 5 cos (2 x) + 5

3 cot (θ) = 3

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