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

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

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

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

x = \frac{1}{2}

Solution steps

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

Rewrite using trig identities

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

Apply trig inverse properties

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

Solve

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

x = \frac{1}{2}

Verify solutions by plugging them into the original equation

x = \frac{1}{2}

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

(cos (x) - 3) (cos (x) + 1) = 0

4 tan^{2} (x) - 16 tan (x) + 7 = 0

1 - cos (x) = 0.5

arctan (100 x) - arctan (x) = 4 5^{\circ}

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