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1)3/2cos2x+1,5sin^2 x-1
2)3sin^2x+1-3cos^2 x
3)-7/2 cos 2x-cos x+3,5 cos^2 x
4)5-20sin^2 a *cos ^2 a ,если sin 2a=-1/5
11)найдите sin ^2 a,если cos2a=1/5
12)sin2x*tgx-sin^2x+1
1)3/2cos2x+1,5sin^2 x-1
2)3sin^2x+1-3cos^2 x
3)-7/2 cos 2x-cos x+3,5 cos^2 x
4)5-20sin^2 a *cos ^2 a ,если sin 2a=-1/5
11)найдите sin ^2 a,если cos2a=1/5
12)sin2x*tgx-sin^2x+1
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Answers & Comments
1) 3/2cos2x + 1,5sin² x - 1 = 1,5cos2x + 1,5sin² x - 1 = 1,5(cos2x + sin² x) - 1 = 1,5(1 - 2sin²x + sin² x) - 1 = 1,5(1 - sin²x) - 1 = 1,5cos²x - 1.
2) 3sin²x + 1 - 3cos² x = 3sin²x - 3cos² x + 1 = -3(cos² x - sin²x) + 1 = -3cos2x+ 1
3) -7/2 cos 2x - cos x + 3,5cos² x = -3,5 cos 2x + 3,5cos² x - cos x = -3,5 (cos 2x - cos² x) - cos x = -3,5 (2cos²x - 1 - cos² x) - cos x = -3,5 (cos²x - 1) - cos x = 3,5 (1 - cos²x) - cos x = 3,5 sin²x - cos x
4) 5 - 20sin² a · cos²a ,если sin 2a=-1/5
5 - 20sin² a · cos²a = 5(1 - 4sin² a · cos²a) = 5(1 - sin2a) = 5(1 - (-1/5)) = 5 + 1 = 6.
11) найдите sin²a, если cos2a = 1/5
sin²a = (1 - cos2a)/2 = (1 - 1/5)/2 = (1 - 0,2)/2 = 0,8 / 2 = 0,4.
12) sin2x · tgx - sin²x + 1 = 2sinx · cosx · (sinx/cosx) - sin²x + 1 = 2sinx · sinx - sin²x + 1 = 2sin²x - sin²x + 1 = sin²x + 1