доказать тождество:
1) 3cos 2α – sin^2 α + cos^2 α = 2cos 2α
2) (Sin 5α – sin 3α) / 2cos 4α = sinα
упростить:
Cos^2 (π-α) – cos^2 ( П/2 - α)
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доказать тождество:
1) 3cos 2α – sin^2 α + cos^2 α = 2cos 2α
2) (Sin 5α – sin 3α) / 2cos 4α = sinα
упростить:
Cos^2 (π-α) – cos^2 ( П/2 - α)
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1.3cos 2α – sin^2 α + cos^2 α = 2cos 2α
3cos 2α – 2cos 2α - sin^2 α + cos^2 α = 0
3cos 2α – 2cos 2α -(1-cosα)/2+(1+cosα)/2=0
6cos 2α – 4cos 2α -1+cosα+1+cosα=0
6cos 2α – 4cos 2α + 2cosα=0
2cos 2α =0
cos 2α =0
2α= П/2+ Пn, n Z
α= П/4+ Пn/2, n Z
2.(Sin 5α – sin 3α) / 2cos 4α = sinα
sin 5α – sin 3α = 2cos 4αsinα
sin 5α – sin 3α =- sin 3α+sin 5α
0=0
Cos^2 (π-α) – cos^2 ( П/2 - α)=Cos^2α – sin^2 α=cos2 α