Rút gọn biểu thức: M=\(\left(1-\sin^2\alpha\right)\cot^2\alpha+\left(1-\cot^2\alpha\right)\)
Rút gọn biểu thức:
\(B=\left(1+tan^2\alpha\right)\left(1-sin^2\alpha\right)-\left(1+cot^2\alpha\right)\left(1-cos^2\alpha\right)\)
\(B=\left(1+\dfrac{sin^2a}{cos^2a}\right).cos^2a-\left(1+\dfrac{cos^2a}{sin^2a}\right).sin^2a\)
\(=\dfrac{\left(sin^2a+cos^2a\right)}{cos^2a}.cos^2a-\left(\dfrac{sin^2a+cos^2a}{sin^2a}\right).sin^2a\)
\(=1-1=0\)
Rút gọn các biểu thức sau:
a) \(\frac{1}{{\tan \alpha + 1}} + \frac{1}{{\cot \alpha + 1}}\)
b) \(\cos \left( {\frac{\pi }{2} - \alpha } \right) - \sin \left( {\pi + \alpha } \right)\)
c) \(\sin \left( {\alpha - \frac{\pi }{2}} \right) + \cos \left( { - \alpha + 6\pi } \right) - \tan \left( {\alpha + \pi } \right)\cot \left( {3\pi - \alpha } \right)\)
\(a,\dfrac{1}{tan\alpha+1}+\dfrac{1}{cot\alpha+1}\\ =\dfrac{cot\alpha+1+tan\alpha+1}{\left(tan\alpha+1\right)\left(cot\alpha+1\right)}\\ =\dfrac{tan\alpha+cot\alpha+2}{tan\alpha\cdot cot\alpha+tan\alpha+cot\alpha+1}\\ =\dfrac{tan\alpha+cot\alpha+2}{tan\alpha+cot\alpha+2}\\ =1\)
\(b,cos\left(\dfrac{\pi}{2}-\alpha\right)-sin\left(\pi+\alpha\right)\\ =sin\alpha+sin\alpha\\ =2sin\alpha\)
\(c,sin\left(\alpha-\dfrac{\pi}{2}\right)+cos\left(-\alpha+6\pi\right)-tan\left(\alpha+\pi\right)cot\left(3\pi-\alpha\right)\\ =-sin\left(\dfrac{\pi}{2}-\alpha\right)+cos\left(\alpha\right)-tan\left(\alpha\right)cot\left(\pi-\alpha\right)\\ =-cos\left(\alpha\right)+cos\left(\alpha\right)+tan\left(\alpha\right)\cdot cot\left(\alpha\right)\\ =1\)
Rút gọn các biểu thức:
a)\(\left(\sin\alpha+\cos\alpha\right)^2+\left(\sin\alpha-\cos\alpha\right)^2\)
b)\(\cot^2\alpha-\cos^2\alpha.\cot^2\alpha\)
c)\(\sin\alpha.\cos\alpha\left(\tan\alpha+\cot\alpha\right)\)
d)\(\tan^2\alpha-\sin^2\alpha.\tan^2\alpha\)
a) khai triển được 2sin2+2cos2=2(sin2+cos2=2.1=2
b)cot2-cos2.cot2=cot2(1-cos2)=cot2.sin2=cos2/sin2.sin2=cos2
c)sin.cos(tan+cot)=sin.cos.tan+sin.cos.cot=sin.cos.sin/cos+sin.cos.cos/sin=sin2+cos2=1
d)tan2-tan2.sin2=tan2(1-sin2)=tan2.cos2=sin2/cos2.cos2=sin2
1/Rút gọn :
\(G=\left(1-sin^2x\right)cot^2x+1-cot^2x\)
2/ Nếu \(tan\alpha+cot\alpha=2\) thì \(tan^2\alpha+cot^2\alpha\) bằng bao nhiêu?
\(G=cot^2x-sin^2x.cot^2x+1-cot^2x=1-sin^2x.cot^2x\)
\(=1-sin^2x.\dfrac{cos^2x}{sin^2x}=1-cos^2x=sin^2x\)
2.
\(tana+cota=2\Rightarrow\left(tana+cota\right)^2=4\)
\(\Rightarrow tan^2a+cot^2a+2tana.cota=4\)
\(\Rightarrow tan^2a+cot^2a+2=4\)
\(\Rightarrow tan^2a+cot^2a=2\)
Chứng minh đẳng thức:
\(\left(\sin^2\alpha-\cos^2\alpha+1\right)\frac{\cot^2\alpha}{2}-\left(1+\cot^2\alpha\right)\left(1-\cot^2\alpha\right)=-\sin^2\alpha\)
rút gọn
a)A=\(\frac{1+2cos\alpha.sin\alpha}{cos^2\alpha-sin^2\alpha}\)
b)B=\(\left(1+\cot^2\alpha\right)\left(1-sin^2\alpha\right)\)-\(\left(1+\cot^2\alpha\right)\left(1-\cos^2\alpha\right)\)
c)C=\(\sin^6\alpha+\cos^6\alpha\)+\(3\sin^2\alpha.cos^2\alpha\)
đơn giản biểu thức:
a, \(\left(\frac{sin\alpha+tan\alpha}{cos\alpha+1}\right)^2+1\)
b, \(tan\alpha\left(\frac{1+cos^2\alpha}{sin\alpha}-sin\alpha\right)\)
c, \(\frac{cot^2\alpha-cos^2\alpha}{cot^2a}+\frac{sin\alpha.cos\alpha}{cot\alpha}\)
\(a=\left(\frac{sina+\frac{sina}{cosa}}{cosa+1}\right)^2+1=\left(\frac{sina\left(cosa+1\right)}{cosa\left(cosa+1\right)}\right)^2+1\)
\(=tan^2a+1=\frac{1}{cos^2a}\)
\(b=\frac{sina}{cosa}\left(\frac{1+cos^2a-sin^2a}{sina}\right)=\frac{sina}{cosa}\left(\frac{2cos^2a}{sina}\right)=2cosa\)
\(c=1-\frac{cos^2a}{cot^2a}+\frac{sina.cosa}{\frac{cosa}{sina}}=1-cos^2a.\frac{sin^2a}{cos^2a}+\frac{sin^2a.cosa}{cosa}\)
\(=1-sin^2a+sin^2a=1\)
Rút gọn biểu thức:
\(A=\sin^210+\sin^220+\sin^230+\sin^280+\sin^270+\sin^260\)
\(B=\left(1+\tan^2\alpha\right)\left(1-\sin^2\alpha\right)+\left(1+\cot^2\alpha\right)\left(1-\cos^2\alpha\right)\)
\(A=sin^210+sin^220+sin^230+sin^280+sin^270+sin^260=sin^210+sin^220+sin^230+cos^210+cos^220+cos^230=1+1+1=3\)\(B=\left(1+tan^2\alpha\right)\left(1-sin^2\alpha\right)+\left(1+cot^2\alpha\right)\left(1-cos^2\alpha\right)=\dfrac{1}{cos^2\alpha}.cos^2\alpha+\dfrac{1}{sin^2\alpha}.sin^2\alpha=1+1=2\)
rút gọn biểu thức
a) \(\left(Sin\alpha+Cos\alpha\right)^2+\left(Sin\alpha-Cos\alpha\right)^2\)
b) \(Sin\alpha.cos\alpha\left(tan\alpha+cot\alpha\right)\)
c) \(cot^2\alpha-Cos^2\alpha\times Cot^2\alpha\)
d) \(tan^2\alpha-Sin^2\alpha\times tan^2\alpha\)
ai giúp e mấy câu này với ạ !!!
tui rất thích lượng giác:
a) = s2 + 2s.c +c2 +s2- 2s.c + c2 =1+1=2
b) = s.c(s/c + c/s) = s.c(s2 + c2) / s.c = 1
.............................bài nào cx dễ
( k có việc j khó, chỉ sợ lòng k bền....)