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Last updated at Sept. 3, 2021 by Teachoo
Transcript
Ex 3.3, 13 Prove that cos2 2𝑥 – cos2 6𝑥 = sin4𝑥 sin8𝑥 Solving L.H.S. cos2 2x – cos2 6x Using a2 – b2 = (a + b) (a - b) = (cos 2x + cos 6x) (cos 2x – cos 6x) Lets calculate (cos 2x + cos 6x) and (cos 2x + cos 6x) separately Hence cos2 2𝑥 – cos2 6𝑥 = (cos2𝑥 + cos6𝑥) (cos2𝑥 – 6𝑥) = (2 cos〖4𝑥 cos〖(−2𝑥)〗 〗 ) (−2 sin4𝑥 (sin〖(−2𝑥)〗 )) = (2 cos〖4𝑥 cos〖(2𝑥)〗 〗 ) (−2 sin4𝑥 (〖−sin〗〖(2𝑥)〗 )) = (2 cos〖4𝑥 cos〖(2𝑥)〗 〗 ) (2 sin4𝑥 sin〖(2𝑥)〗 ) = (2 sin4𝑥 cos4𝑥) (2 sin2𝑥 cos2𝑥) = sin8𝑥 sin4𝑥 = R.H.S. Hence, L.H.S. = R.H.S. Hence proved
(x + y) formula
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