Question

Sin^2 6x - sin^2 4x = sin 2x sin 10x
pls prove it

Answer 1

sin²(6x) - sin²(4x) = sin(2x)sin(10x)
¹/₂[1 - cos(12x)] - ¹/₂[1 - cos(8x)] = ¹/₂[cos(2x - 10x) - cos(2x + 10x)]
[¹/₂ - ¹/₂cos(12x)] - [¹/₂ - ¹/₂cos(8x)] = ¹/₂[cos(-8x) - cos(12x)]
[¹/₂ - ¹/₂] + [⁻¹/₂cos(12x) + ¹/₂cos(8x)] = ¹/₂[cos(8x) - cos(12x)
⁻¹/₂cos(12x) + ¹/₂cos(8x) = ¹/₂cos(8x) - ¹/₂cos(12x)
- ¹/₂cos(8x) - ¹/₂cos(8x)
⁻¹/₂cos(12x) = ⁻¹/₂cos(12x)