Kẻ đường cao AH

Áp dụng PTG: \(BC=\sqrt{AB^2+AC^2}=10\left(cm\right)\)

Áp dụng HTL: \(BH=\dfrac{AB^2}{BC}=\dfrac{18}{5}\left(cm\right);AH=\dfrac{AB\cdot AC}{BC}=\dfrac{24}{5}\left(cm\right)\)

Vì AD là p/g nên \(\dfrac{BD}{DC}=\dfrac{AB}{AC}=\dfrac{3}{4}\Rightarrow BD=\dfrac{3}{4}DC\)

Mà \(BD+DC=BC=10\Rightarrow\dfrac{7}{4}DC=10\Rightarrow DC=\dfrac{40}{7}\left(cm\right)\)

\(\Rightarrow BD=\dfrac{30}{7}\left(cm\right)\)

\(\Rightarrow HD=BD-BH=\dfrac{30}{7}-\dfrac{18}{5}=\dfrac{24}{35}\)

Áp dụng PTG: \(AD=\sqrt{AH^2+HD^2}=\sqrt{\left(\dfrac{24}{35}\right)^2+\left(\dfrac{24}{5}\right)^2}=\dfrac{24\sqrt{2}}{7}\approx4,85\left(cm\right)\)

Đề bài là: Tính cos2x 

Cảm ơn mn nhiều ạ!

`sin3x sinx+sin(x-π/3) cos (x-π/6)=0`

`<=> 1/2 (cos2x - cos4x) + 1/2(-sin π/6 + sin (2x-π/2)=0`

`<=> cos2x-cos4x-1/2+ sin(2x-π/2)=0`

`<=>cos2x-cos4x-1/2+ sin2x .cos π/2 - cos2x. sinπ/2=0`

`<=> cos2x - cos4x - cos2x = 1/2`

`<=> cos4x = cos(2π)/3`

`<=>` \(\left[{}\begin{matrix}4x=\dfrac{2\text{π}}{3}+k2\text{π}\\4x=\dfrac{-2\text{π}}{3}+k2\text{π}\end{matrix}\right.\)

`<=>` \(\left[{}\begin{matrix}x=\dfrac{\text{π}}{6}+k\dfrac{\text{π}}{2}\\x=-\dfrac{\text{π}}{6}+k\dfrac{\text{π}}{2}\end{matrix}\right.\)

\(sin3x.sinx+sin\left(x-\dfrac{\pi}{3}\right)cos\left(x-\dfrac{\pi}{6}\right)=0\)

\(\Leftrightarrow\dfrac{1}{2}cos2x-\dfrac{1}{2}cos4x+\dfrac{1}{2}sin\left(2x-\dfrac{\pi}{2}\right)+\dfrac{1}{2}sin\left(-\dfrac{\pi}{6}\right)=0\)

\(\Leftrightarrow\dfrac{1}{2}cos2x-\dfrac{1}{2}cos4x-\dfrac{1}{2}cos2x-\dfrac{1}{4}=0\)

\(\Leftrightarrow cos4x+\dfrac{1}{2}=0\)

\(\Leftrightarrow2cos^22x-1+\dfrac{1}{2}=0\)

\(\Leftrightarrow cos^22x=\dfrac{1}{4}\)

\(\Rightarrow cos2x=\pm\dfrac{1}{2}\)

1. Turn on (please+Vo)

2. Turned / off (was chia qk)

3. Look for

4. Got up (because S+ had+V3/ed, S+V2/ed)

5. Ran into( hai hd lien tiep)

6. Goes on (after S+V2/ed, S+Vht)

1:

a: Khi m=1 thì (1) sẽ là x^2+2x-5=0

=>\(x=-1\pm\sqrt{6}\)

b: Δ=(2m)^2-4(-2m-3)

=4m^2+8m+12

=4m^2+8m+4+8=(2m+2)^2+8>=8>0

=>Phương trình luôn có hai nghiệm phân biệt

2:

Thay x=-1 và y=2 vào (P), ta được:

a*(-1)^2=2

=>a=2

E tk nha: