निम्नलिखित को सिद्ध कीजिए:
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Step-by-step explanation:
sin2x + 2 sin4x + sin6x = 4 cos^{2}x sin4x
L.H.S. = sin2x + 2 sin4x + sin6x
= ( sin2x + sin6x )+ 2 sin4x
= 2 sin( + 2 sin4x
(∵ sinA + sinB = )
= 2 sin(4x) cos(-2x) + 2 sin4x
= 2 sin4x ( cos2x + 1 ) [∵cos(-θ) = cosθ ]
= 2 sin4x ( 2 cos^{2}x ) [ 1+cos2x = 2cos^{2}x]
=
= R.H.S.
L.H.S. = R.H.S.
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