determine the least positive angle sin^2x+cos^2x+tan^2x=4/3?
回答 (2)
2018-11-27 6:31 pm
sin²(x) + cos²(x) + tan²(x) = 4/3 → recall: sin²(x) + cos²(x) = 1
1 + tan²(x) = 4/3
tan²(x) = (4/3) - 1
tan²(x) = 1/3
tan²(x) = (± 1/√3)²
tan(x) = ± 1/√3
tan(x) = ± (√3)/3
First case: tan(x) = (√3)/3
x = π/6
Second case: tan(x) = - (√3)/3
x = - π/6
1 + tan²(x) = 4/3
tan²(x) = (4/3) - 1
tan²(x) = 1/3
tan²(x) = (± 1/√3)²
tan(x) = ± 1/√3
tan(x) = ± (√3)/3
First case: tan(x) = (√3)/3
x = π/6
Second case: tan(x) = - (√3)/3
x = - π/6
2018-11-27 1:46 pm
so cos ²x = 3 / 4====> cos x = ±√3 / 2 ===> for you π / 6
收錄日期: 2021-04-24 01:15:08
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https://hk.answers.yahoo.com/question/index?qid=20181127054138AAOOR8g