What is the general solution for arcsin(3x)+arcsin(x)=60 ?

The general solution for arcsin(3x)+arcsin(x)=60 is x=(sqrt(3))/(2sqrt(13))

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arcsin(3x)+arcsin(x)=60

arcsin (3 x) + arcsin (x) = 6 0^{\circ}

x = \frac{3}{2 13}

Solution steps

arcsin (3 x) + arcsin (x) = 6 0^{\circ}

Rewrite using trig identities

arcsin (3 x 1 - x^{2} + x 1 - (3 x)^{2}) = 6 0^{\circ}

Apply trig inverse properties

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

Solve

3 x 1 - x^{2} + x 1 - (3 x)^{2} = \frac{3}{2} : x = \frac{3}{2 13}

x = \frac{3}{2 13}

Verify solutions by plugging them into the original equation

x = \frac{3}{2 13}

cos (x) + sin (x) = \frac{1}{2}

4 cos^{2} (2 x) - 4 cos (2 x) + 1 = 0

cos (θ) = \frac{2}{13}

4 sin (x - π) + 2 = 0

\frac{1}{2} tan (2 x) = tan (x)

What is the general solution for arcsin(3x)+arcsin(x)=60 ?
The general solution for arcsin(3x)+arcsin(x)=60 is x=(sqrt(3))/(2sqrt(13))