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Sin2 6x - sin2 4x = …

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Sin2 6x - sin2 4x = sin 2x sin10x
  • 2 answers

Ff Sedn 4 years, 5 months ago

Hi

Gaurav Seth 4 years, 5 months ago

LHS = sin²(6x) - sin²(4x)
Use the formula,
(a² - b²) = (a - b)(a + b)
= (sin6x -sin4x)(sin6x +sin4x)
Now,
Use the formula,
sinC + sinD = 2sin(C+D)/2.cos(C-D)/2
sinC - sinD = 2cos(C+D)/2.sin(C-D)/2

={2cos(6x+4x)/2.sin(6x-4x)/2}{2sin(6x+4x)/2.cos(6x-4x)/2}
={2cos5x.sinx}{2sin5x.cosx}
={2sin5x.cos5x}{2sinx.cosx}

Use the formula,
sin2A = 2sinA.cosA

= sin2(5x).sin2(x)
= sin10x.sin2x =RHS

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