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2(sin 6?+cos6?) - 3(sin4?+cos4?)+1 = 0
Ans: (Sin2?)3 + (Cos2?)3-3 (Sin4?+(Cos4?)+1=0
Consider (Sin2?)3 +(Cos2?)3
⇒(Sin2?+Cos2?)3-3 Sin2?Cos2?( Sin2?+Cos2?)
= 1- 3Sin2? Cos2?
Sin4?+Cos4?(Sin2?)2+(Cos2?)2
= (Sin2?+Cos2?)2-2 Sin2? Cos2?
= 1- 2 Sin2? Cos2?
= 2(Sin6?+Cos6?)-3(Sin4?+Cos4?) +1
= 2 (1-3 Sin2? Cos2?)-3 (1-2 Sin2?+Cos2?)+1
writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
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