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ученик1851
@ученик1851
September 2021
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помогите 171-172 пожалуйста 20 балов
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kopatel228
171.
1) Sin^2x + Cos^2x + tg^2x - 1/Cos^2x
1/Cos^2x = Sin^2x + Cos^2x / Cos^2x (деление на Cos^2x) = tg^2x + 1
Sin^2x + Cos^2x = 1
1 + tg^2x - tg^2x - 1 = 0
2) 2 - 1/Sin^2x + Ctg^2x
1/Sin^2x = Sin^2x + Cos^2x / Sin^2x (деление на Sin^2x) = 1 + Ctg^2x
2 - 1 - Ctg^2x + Ctg^2x = 1
172.
1) Cosx = 1/2
Sinx = √1 - Cos^2x = √1 - 1/4 = √3/2
tgx = Sinx/Cosx = √3/2 * 2/1 = √3
2) Sinx = √3/2
Cosx = √1 - Sin^2x = √1 - 3/4 = 1/2
tgx = Sinx/Cosx = √3/2 * 2/1 = √3
3) Sinx = 1/4
Cosx = √1 - Sin^2x = √1 - 1/16 = √15/4
tgx = Sinx/Cosx = 1/4 * 4/√15 = 1/√15
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Answers & Comments
1) Sin^2x + Cos^2x + tg^2x - 1/Cos^2x
1/Cos^2x = Sin^2x + Cos^2x / Cos^2x (деление на Cos^2x) = tg^2x + 1
Sin^2x + Cos^2x = 1
1 + tg^2x - tg^2x - 1 = 0
2) 2 - 1/Sin^2x + Ctg^2x
1/Sin^2x = Sin^2x + Cos^2x / Sin^2x (деление на Sin^2x) = 1 + Ctg^2x
2 - 1 - Ctg^2x + Ctg^2x = 1
172.
1) Cosx = 1/2
Sinx = √1 - Cos^2x = √1 - 1/4 = √3/2
tgx = Sinx/Cosx = √3/2 * 2/1 = √3
2) Sinx = √3/2
Cosx = √1 - Sin^2x = √1 - 3/4 = 1/2
tgx = Sinx/Cosx = √3/2 * 2/1 = √3
3) Sinx = 1/4
Cosx = √1 - Sin^2x = √1 - 1/16 = √15/4
tgx = Sinx/Cosx = 1/4 * 4/√15 = 1/√15