sin(a+b)sin(a-b)=0

Solution for sin(a+b)sin(a-b)=0 equation:

Simplifying
sin(a + b) * sin(a + -1b) = 0

Reorder the terms for easier multiplication:
ins * ins(a + b)(a + -1b) = 0

Multiply ins * ins
i2n2s2(a + b)(a + -1b) = 0

Multiply (a + b) * (a + -1b)
i2n2s2(a(a + -1b) + b(a + -1b)) = 0
i2n2s2((a * a + -1b * a) + b(a + -1b)) = 0

Reorder the terms:
i2n2s2((-1ab + a2) + b(a + -1b)) = 0
i2n2s2((-1ab + a2) + b(a + -1b)) = 0
i2n2s2(-1ab + a2 + (a * b + -1b * b)) = 0
i2n2s2(-1ab + a2 + (ab + -1b2)) = 0

Reorder the terms:
i2n2s2(-1ab + ab + a2 + -1b2) = 0

Combine like terms: -1ab + ab = 0
i2n2s2(0 + a2 + -1b2) = 0
i2n2s2(a2 + -1b2) = 0
(a2 * i2n2s2 + -1b2 * i2n2s2) = 0
(a2i2n2s2 + -1b2i2n2s2) = 0

Solving
a2i2n2s2 + -1b2i2n2s2 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add 'b2i2n2s2' to each side of the equation.
a2i2n2s2 + -1b2i2n2s2 + b2i2n2s2 = 0 + b2i2n2s2

Combine like terms: -1b2i2n2s2 + b2i2n2s2 = 0
a2i2n2s2 + 0 = 0 + b2i2n2s2
a2i2n2s2 = 0 + b2i2n2s2
Remove the zero:
a2i2n2s2 = b2i2n2s2

Divide each side by 'i2n2s2'.
a2 = b2

Simplifying
a2 = b2

Take the square root of each side:
a = {-1b, b}