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) + arcsin (x)

Use the Sum to Product identity:

arcsin (s) + arcsin (t) = arcsin (s 1 - t^{2} + t 1 - s^{2})

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

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

Check the solutions by plugging them into

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

Remove the ones that don't agree with the equation.

No Solution for x \in R

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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}