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Citrus2011 [14]
3 years ago
8

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

Mathematics
1 answer:
Marina86 [1]3 years ago
3 0
                          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)
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