What is the general solution for sin(39)+sin(21)=sin(a) ?

The general solution for sin(39)+sin(21)=sin(a) is No Solution for a\in\mathbb{R}

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sin(39)+sin(21)=sin(a)

sin (3 9^{\circ}) + sin (2 1^{\circ}) = sin (a^{\circ})

No Solution for a \in R

Solution steps

sin (3 9^{\circ}) + sin (2 1^{\circ}) = sin (a^{\circ})

Switch sides

sin (a^{\circ}) = sin (3 9^{\circ}) + sin (2 1^{\circ})

Apply trig inverse properties

a^{\circ} = arcsin (sin (3 9^{\circ}) + sin (2 1^{\circ})) + 36 0^{\circ} n, a^{\circ} = 18 0^{\circ} - arcsin (sin (3 9^{\circ}) + sin (2 1^{\circ})) + 36 0^{\circ} n

No Solution for a \in R

arctan (4 x - 4) = - 1

tan^{2} (x + \frac{π}{6}) = 3

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{3}{2}

3 cos (2 x) - 2 cos (x) - 1 = 0

sin (3 π x) = 0

What is the general solution for sin(39)+sin(21)=sin(a) ?
The general solution for sin(39)+sin(21)=sin(a) is No Solution for a\in\mathbb{R}