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

The general solution for arcsin(2x)+arcsin(x)=(2pi)/3 is No Solution for x\in\mathbb{R}

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

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

No Solution for x \in R

Solution steps

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

Rewrite using trig identities

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

- \frac{π}{2} \leq arcsin (x) \leq \frac{π}{2}

No Solution

Verify solutions by plugging them into the original equation

No Solution for x \in R

2 sin (4 x) + 8 = 0

sin (x - 53.1 3^{\circ}) = - \frac{2}{5}

2 csc (x) + 2 = 0

1 + cos (x) = 3 cos (x)

cos (θ) = \frac{14}{16}

What is the general solution for arcsin(2x)+arcsin(x)=(2pi)/3 ?
The general solution for arcsin(2x)+arcsin(x)=(2pi)/3 is No Solution for x\in\mathbb{R}