Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesTrigonometrical ratios of sum and difference of two and three angles
MediumProve that $\sin^{2} 6x - \sin^{2} 4x = \sin 2x \sin 10x$.
(N/A) We use the identity $\sin^{2} A - \sin^{2} B = \sin(A+B) \sin(A-B)$.
$L.H.S. = \sin^{2} 6x - \sin^{2} 4x$
$= \sin(6x + 4x) \sin(6x - 4x)$
$= \sin(10x) \sin(2x)$
$= \sin 2x \sin 10x$
$= R.H.S.$
$L.H.S. = \sin^{2} 6x - \sin^{2} 4x$
$= \sin(6x + 4x) \sin(6x - 4x)$
$= \sin(10x) \sin(2x)$
$= \sin 2x \sin 10x$
$= R.H.S.$
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