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22.06.2019 •
History
Which ethnicities were under the control of the hapsburg empire in the 1800s? select all that apply austrians slavs french portuguese hungarians czechs italians dutch (answers austrians,slavs,hungarian,czechs,italians 100% correct your welcome)
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Ответ:
Explanation:
Given the trigonometry expression sin⁴θ+cos⁴θ , the minimum value of the expression occurs at when θ = 0° and maximum value occurs at when θ = 90°.
From trigonometry identity;
sin²θ+cos²θ = 1
square both sides;
(sin²θ+cos²θ)² = 1²
open the parenthesis;
sin⁴θ+2sin²θcos²θ+cos⁴θ = 1
subtract 2sin²θcos²θ from both sides;
sin⁴θ+2sin²θcos²θ+cos⁴θ-2sin²θcos²θ = 1-2sin²θcos²θ
sin⁴θ+cos⁴θ = 1-2sin²θcos²θ
Since the minimum value occur at θ = 0°, substitute θ = 0° into the right hand side of the resulting expression as shown;
sin⁴θ+cos⁴θ = 1-2sin²(0)cos²(0)
sin⁴θ+cos⁴θ = 1-2(0)(1)
sin⁴θ+cos⁴θ = 1-0
sin⁴θ+cos⁴θ = 1
Hence the minimum value of sin⁴θ+cos⁴θ is 1
For the maximum value;
Since the maximum value occur at θ = 90°, substitute θ = 90° into the right hand side of the resulting expression as shown;
sin⁴θ+cos⁴θ = 1-2sin²(90)cos²(90)
sin⁴θ+cos⁴θ = 1-2(1)(0)
sin⁴θ+cos⁴θ = 1-0
sin⁴θ+cos⁴θ = 1
Hence the maximum value of sin⁴θ+cos⁴θ is also 1