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willzymustdie
@willzymustdie
August 2021
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УПРОСТИТЕ ВЫРАЖЕНИЕ ctg²A (1 - cos2A)² + cos² 2A
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Verified answer
Ctg²a(1 - Cos2a)² + Cos²2a = Cos²a/Sin²a(Sin²a + Cos²a - Cos²a + Sin²a)² +
+ Cos²2a = Cos²a/Sin²a(2Sin²a)² + Cos²2a = Cos²a/Sin²a * 4Sin^4a + Cos²2a =
= 4Sin²aCos²a + ( 2Cos²a - 1)² = 4Sin²aCos²a + 4Cos^4a - 4Cos²a + 1 =
= (4Sin²aCos²a + 4Cos^4a) - 4Cos²a + 1 = 4Cos²a(Sin²a+ Cos²a) - 4Cos²a + 1 =4 Cos²a - 4Cos²a + 1 = 1
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Answers & Comments
Verified answer
Ctg²a(1 - Cos2a)² + Cos²2a = Cos²a/Sin²a(Sin²a + Cos²a - Cos²a + Sin²a)² ++ Cos²2a = Cos²a/Sin²a(2Sin²a)² + Cos²2a = Cos²a/Sin²a * 4Sin^4a + Cos²2a =
= 4Sin²aCos²a + ( 2Cos²a - 1)² = 4Sin²aCos²a + 4Cos^4a - 4Cos²a + 1 =
= (4Sin²aCos²a + 4Cos^4a) - 4Cos²a + 1 = 4Cos²a(Sin²a+ Cos²a) - 4Cos²a + 1 =4 Cos²a - 4Cos²a + 1 = 1