Tính sin2a, cos2a, tan2a, biết:
a) sina = -0,6 và π < a < ;
b) cosa = - và
< a < π
c) sina + cosa = và
< a < π
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(Sina -cosa)^2 =1:25
<=> sin^2a +cos^2a -2sina.cosa =1:25
Ta có sin^2a+cos^2a = 1
<=> 1-2 sina.cosa =1:25
2sina.cosa =24:25
CT : sin2a= 2sina.cosa=24:25
Có sin^2 .2a + co^2.2a = 1
(24:25)^2 + cos^2.2a =1
Từ đây rút cos 2a = căn 1-(24:25)^2 =... bạn tự làm tiếp nha !
\(\left(1+tan^2a\right)\left(1-sin^2a\right)-\left(1+cot^2a\right)\left(1-cos^2a\right)\)
\(=\left(1+\dfrac{sin^2a}{cos^2a}\right).cos^2a-\left(1+\dfrac{cos^2a}{sin^2a}\right).sin^2a\)
\(=cos^2a+sin^2a-sin^2a-cos^2a=\)\(0\)
Vậy B=0
\(\frac{sina+sin3a+sin2a}{cosa+cos3a+cos2a}=\frac{2sin2a.cosa+sin2a}{2cos2a.cosa+cos2a}=\frac{sin2a\left(2cosa+1\right)}{cos2a\left(2cosa+1\right)}=\frac{sin2a}{cos2a}=tan2a\)
\(cos^2\left(a-\frac{\pi}{4}\right)-sin^2\left(a-\frac{\pi}{4}\right)=cos\left(2a-\frac{\pi}{2}\right)\)
\(=cos\left(\frac{\pi}{2}-2a\right)=sin2a\)
\(A=cos^2a+cos^2b+2cosa.cosb+sin^2a+sin^2b+2sina.sinb\)
\(=cos^2a+sin^2a+cos^2b+sin^2b+2\left(cosa.cosb+sina.sinb\right)\)
\(=2+2cos\left(a-b\right)=2+2cos\frac{\pi}{3}=3\)
\(\left(cosa+sina\right)^2=\frac{36}{25}\Leftrightarrow1+2sina.cosa=\frac{36}{25}\)
\(\Rightarrow sin2a=\frac{36}{25}-1=\frac{11}{25}\)
\(cos2a=cos^2a-sin^2a=\left(cosa-sina\right)\left(cosa+sina\right)>0\)
\(\Rightarrow cos2a=\sqrt{1-sin^22a}=\frac{6\sqrt{14}}{25}\)
a) π < a <
=> sina < 0, cosa < 0, tana > 0
sin2a = 2sinacosa = 2(-0,6)(-
) = 0,96
cos2a = cos2 a – sin2 a = 1 – 2sin2 a = 1 - 0,72 = 0,28
tan2a =
≈ 3,1286
b)
< a < π => sina > 0, cosa < 0
sina =![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Csqrt%7B1-%5Cleft%20%28%20%5Cfrac%7B5%7D%7B13%7D%20%5Cright%20%29%5E%7B2%7D%7D%3D%5Cfrac%7B12%7D%7B13%7D)
sin2a = 2sinacosa = 2.![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7B12%7D%7B13%7D%5Cleft%20%28%20-%5Cfrac%7B5%7D%7B13%7D%20%5Cright%20%29%3D-%5Cfrac%7B120%7D%7B169%7D)
cos2a = 2cos2a - 1 = 2
- 1 = -![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7B119%7D%7B169%7D)
tan2a =![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7Bsin2a%7D%7Bcos2a%7D%3D%5Cfrac%7B120%7D%7B119%7D)
c)
< a < π =>
< 2a < 2π => sin2a < 0, cos2a > 0, tan2a < 0
sin2a =
- 1 = -0,75
cos2a =![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Csqrt%7B1-%5Cleft%20%28%20%5Cfrac%7B3%7D%7B4%7D%20%5Cright%20%29%5E%7B2%7D%7D%3D%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D)
tan2a = -