giải pt cos^2 (x-30)=3/4

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Asked: Tháng Mười 23, 20202020-10-23T18:00:20+00:00 2020-10-23T18:00:20+00:00In: Môn Toán

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Bo · Answer 1 · 2020-10-23T18:01:27+00:00

$\cos^2(x-30^o)=\dfrac{3}{4}$

$\Leftrightarrow \dfrac{1+\cos(2x-60^o)}{2}=\dfrac{3}{4}$

$\Leftrightarrow \cos(2x-60^o)=0,5$

$\Leftrightarrow 2x-60^o=\pm 60^o+k360^o$

$\Leftrightarrow x=60^o+k360^o$ hoặc $x=k180^o$

Orla · Answer 2 · 2020-10-23T18:02:03+00:00

Đáp án:

$\left[\begin{array}{l}x = 60^o + k180^o\\x = k180^o\end{array}\right.(k\in\Bbb Z)$

Giải thích các bước giải:

$\cos^2(x – 30^o) = \dfrac{3}{4}$

$\Leftrightarrow \dfrac{1 + \cos(2x – 60^o)}{2} = \dfrac{3}{4}$

$\Leftrightarrow \cos(2x – 60^o) = \dfrac{1}{2}$

$\Leftrightarrow \left[\begin{array}{l}2x – 60^o = 60^o + k360^o\\2x – 60^o = – 60^o + k360^o\end{array}\right.$

$\Leftrightarrow \left[\begin{array}{l}x = 60^o + k180^o\\x = k180^o\end{array}\right.(k\in\Bbb Z)$