Toán Sin a+cos a= 1/2 Tính sin2a,cos2a,tan2a,cot2a 05/10/2021 By Aubrey Sin a+cos a= 1/2 Tính sin2a,cos2a,tan2a,cot2a
Đáp án: $ sin 2a= – \dfrac{3}{4}$ $ cos 2a=±\dfrac{\sqrt7}{4}$ $ tan 2a=±\dfrac{3}{\sqrt7}$ $ cot 2a=±\dfrac{\sqrt7}{3}$ Giải thích cách làm; $(sina+cosa)^2=\frac{1}{4}$ $\Leftrightarrow sin^2a+cos^2a+2sinacosa= \dfrac{1}{4}$ $\Rightarrow sin2a=2sinacosa=\dfrac{1}{4}-1=\dfrac{-3}{4}$ $cos2a=±\sqrt{1-sin^22a}=±\dfrac{\sqrt7}{4}$ $tan2a=\dfrac{sin2a}{cos2a}=±\dfrac{3}{\sqrt7}$ $cot2a=\dfrac{1}{tan2a}=±\dfrac{\sqrt7}{3}$ Trả lời
Đáp án:
$ sin 2a= – \dfrac{3}{4}$
$ cos 2a=±\dfrac{\sqrt7}{4}$
$ tan 2a=±\dfrac{3}{\sqrt7}$
$ cot 2a=±\dfrac{\sqrt7}{3}$
Giải thích cách làm;
$(sina+cosa)^2=\frac{1}{4}$
$\Leftrightarrow sin^2a+cos^2a+2sinacosa= \dfrac{1}{4}$
$\Rightarrow sin2a=2sinacosa=\dfrac{1}{4}-1=\dfrac{-3}{4}$
$cos2a=±\sqrt{1-sin^22a}=±\dfrac{\sqrt7}{4}$
$tan2a=\dfrac{sin2a}{cos2a}=±\dfrac{3}{\sqrt7}$
$cot2a=\dfrac{1}{tan2a}=±\dfrac{\sqrt7}{3}$