Giúp mình vs ạ!!
Tìm \(\alpha\):
a) sin\(\alpha\) = cos\(\alpha\)
b) \(\tan\alpha=\cot\alpha\)
Những câu hỏi liên quan
a) Biết sinα= \(\frac{1}{2}\). Tính cosα, tanα, cotα.
b) Biết cosα= \(\frac{2}{5}\). Tính sinα, tanα, cotα.
c) Biết tanα= 3. Tính cosα, sinα, cotα.
d) Biết cotα=\(\sqrt{3}\). Tính cosα, tanα, sinα.
e) Biết sinα= \(\frac{1}{\sqrt{3}}\). Tính cosα, tanα, cotα.
a) Cho $\cos \alpha=\dfrac{3}{4}$ với $0^{\circ}<\alpha<90^{\circ}$. Tính $A=\dfrac{\tan \alpha+3 \cot \alpha}{\tan \alpha+\cot \alpha}$.
b) Cho $\tan \alpha=\sqrt{2}$. Tính $B=\dfrac{\sin \alpha-\cos \alpha}{\sin ^{3} \alpha+3 \cos ^{3} \alpha+2 \sin \alpha}$.
Chứng minh các đẳng thức sau:
a, sin^4alpha-cos^4alpha+12sin^2alpha
b,dfrac{sin^2alpha+2cos^2alpha-1}{cot^2alpha}sin^2alpha
c, dfrac{1-sin^2alpha.cos^2alpha}{cos^2alpha}-cos^2alphatan^2alpha
d, dfrac{sin^2alpha-tan^2alpha}{cos^2alpha-cot^2alpha}tan^6alpha
e, left(1+cotalpharight)sin^3alpha+left(1+tanalpharight)cos^3alphasinalpha.cosalpha
f,dfrac{left(sinalpha+cosalpharight)^2-1}{cotalpha-sinalpha.cosalpha}2tan^2alpha
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Chứng minh các đẳng thức sau:
a, \(\sin^4\alpha-\cos^4\alpha+1=2\sin^2\alpha\)
b,\(\dfrac{\sin^2\alpha+2\cos^2\alpha-1}{\cot^2\alpha}=\sin^2\alpha\)
c, \(\dfrac{1-\sin^2\alpha.\cos^2\alpha}{\cos^2\alpha}-\cos^2\alpha=\tan^2\alpha\)
d, \(\dfrac{\sin^2\alpha-\tan^2\alpha}{\cos^2\alpha-\cot^2\alpha}=\tan^6\alpha\)
e, \(\left(1+\cot\alpha\right)\sin^3\alpha+\left(1+\tan\alpha\right)\cos^3\alpha=\sin\alpha.\cos\alpha\)
f,\(\dfrac{\left(\sin\alpha+\cos\alpha\right)^2-1}{\cot\alpha-\sin\alpha.\cos\alpha}=2\tan^2\alpha\)
a)
\(\sin ^4a-\cos ^4a+1=(\sin ^2a-\cos ^2a)(\sin ^2a+\cos^2a)+1\)
\(=(\sin ^2a-\cos ^2a).1+1=\sin ^2a-\cos ^2a+\sin ^2a+\cos ^2a\)
\(=2\sin ^2a\)
b) \(\sin ^2a+2\cos ^2a-1=(\sin ^2a+\cos^2a)+\cos ^2a-1\)
\(=1+\cos ^2a-1=\cos ^2a\)
\(\Rightarrow \frac{\sin ^2a+2\cos ^2a-1}{\cot ^2a}=\frac{\cos ^2a}{\cot ^2a}=\frac{\cos ^2a}{\frac{\cos ^2a}{\sin ^2a}}=\sin ^2a\)
c)
\(\frac{1-\sin ^2a\cos ^2a}{\cos ^2a}-\cos ^2a=\frac{1}{\cos ^2a}-\sin ^2a-\cos ^2a\)
\(=\frac{1}{\cos ^2a}-(\sin ^2a+\cos ^2a)=\frac{1}{\cos ^2a}-1\)
\(=\frac{1-\cos ^2a}{\cos ^2a}=\frac{\sin ^2a}{\cos ^2a}=\tan ^2a\)
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d)
\(\frac{\sin ^2a-\tan ^2a}{\cos ^2a-\cot ^2a}=\frac{\sin ^2a-\frac{\sin ^2a}{\cos ^2a}}{\cos ^2a-\frac{\cos ^2a}{\sin ^2a}}\) \(=\frac{\sin ^2a(1-\frac{1}{\cos ^2a})}{\cos ^2a(1-\frac{1}{\sin ^2a})}\)
\(=\frac{\sin ^2a.\frac{\cos ^2a-1}{\cos ^2a}}{\cos ^2a.\frac{\sin ^2a-1}{\sin ^2a}}\) \(=\frac{\sin ^2a.\frac{-\sin ^2a}{\cos ^2a}}{\cos ^2a.\frac{-\cos ^2a}{\sin ^2a}}=\frac{\sin ^6a}{\cos ^6a}=\tan ^6a\)
f)
\(\frac{(\sin a+\cos a)^2-1}{\cot a-\sin a\cos a}=\frac{\sin ^2a+\cos ^2a+2\sin a\cos a-1}{\frac{\cos a}{\sin a}-\sin a\cos a}\)
\(=\sin a.\frac{1+2\sin a\cos a-1}{\cos a-\cos a\sin ^2a}\)
\(=\sin a. \frac{2\sin a\cos a}{\cos a(1-\sin ^2a)}=\sin a. \frac{2\sin a\cos a}{\cos a. \cos^2 a}=\frac{2\sin ^2a}{\cos ^2a}=2\tan ^2a\)
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e)
\((1+\cot a)\sin ^3a+(1+\tan a)\cos ^3a\)
\(=(\sin ^3a+\cos ^3a)+\cot a.\sin ^3a+\tan a.\cos^3a\)
\(=(\sin a+\cos a)(\sin ^2a-\sin a\cos a+\cos ^2a)+\frac{\cos a}{\sin a}.\sin ^3a+\frac{\sin a}{\cos a}.\cos ^3a\)
\(=(\sin a+\cos a)(1-\sin a\cos a)+\cos a\sin ^2a+\sin a\cos ^2a\)
\(=\sin a+\cos a-\sin a\cos a(\sin a+\cos a)+\cos a\sin a(\sin a+\cos a)\)
\(=\sin a+\cos a\)
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25 tháng 7 2021 lúc 14:27
Cho tan\(\alpha\) + cot\(\alpha\) = 2
a, Tính cos\(\alpha\), sin\(\alpha\), tan\(\alpha\), cot\(\alpha\).
b, Tính E = \(\dfrac{sin\alpha.cos\alpha}{tan^2\alpha+cot^2\alpha}\)
Lời giải:
a.
$\tan a+\cot a=2\Leftrightarrow \tan a+\frac{1}{\tan a}=2$
$\Leftrightarrow \frac{\tan ^2a+1}{\tan a}=2$
$\Leftrightarrow \tan ^2a-2\tan a+1=0$
$\Leftrightarrow (\tan a-1)^2=0\Rightarrow \tan a=1$
$\cot a=\frac{1}{\tan a}=1$
$1=\tan a=\frac{\cos a}{\sin a}\Rightarrow \cos a=\sin a$
Mà $\cos ^2a+\sin ^2a=1$
$\Rightarrow \cos a=\sin a=\pm \frac{1}{\sqrt{2}}$
b.
Vì $\sin a=\cos a=\pm \frac{1}{\sqrt{2}}$
$\Rightarrow \sin a\cos a=\frac{1}{2}$
$E=\frac{\sin a.\cos a}{\tan ^2a+\cot ^2a}=\frac{\frac{1}{2}}{1+1}=\frac{1}{4}$
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25 tháng 7 2021 lúc 14:59
Cho sin\(\alpha\) + cos\(\alpha\) =\(\sqrt{2}\)
a, Tính cos\(\alpha\), sin\(\alpha\), tan\(\alpha\), cot\(\alpha\).
b, Tính F = \(sin^5\alpha+cos^5\alpha\)
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....)
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CMR
a)\(\frac{1+\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1-\cos\alpha}\)
b)\(\frac{\tan\alpha+1}{\tan\alpha-1}=\frac{1+\cot\alpha}{1-\cot\alpha}\)
c) \(\tan^2\alpha-\sin^2\alpha=\tan^2\alpha.\sin^2\alpha\)
d)\(\frac{1-4\sin^2\alpha.\cos^2\alpha}{\left(\sin\alpha-\cos\alpha\right)^2}=\left(\sin\alpha+\cos\alpha\right)^2\)
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, \(\frac{cot^2\alpha-cos^2\alpha}{cot^2a}+\frac{sin\alpha.cos\alpha}{cot\alpha}\)
\(a=\left(\frac{sina+\frac{sina}{cosa}}{cosa+1}\right)^2+1=\left(\frac{sina\left(cosa+1\right)}{cosa\left(cosa+1\right)}\right)^2+1\)
\(=tan^2a+1=\frac{1}{cos^2a}\)
\(b=\frac{sina}{cosa}\left(\frac{1+cos^2a-sin^2a}{sina}\right)=\frac{sina}{cosa}\left(\frac{2cos^2a}{sina}\right)=2cosa\)
\(c=1-\frac{cos^2a}{cot^2a}+\frac{sina.cosa}{\frac{cosa}{sina}}=1-cos^2a.\frac{sin^2a}{cos^2a}+\frac{sin^2a.cosa}{cosa}\)
\(=1-sin^2a+sin^2a=1\)
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Giúp mình vs chiều phải nộp bài rồi
a)C 4cos^2alpha-3sin^2alpha.cosfrac{4}{7}
b)cos^2alpha+cos^2beta+cos^2alpha.sin^2beta+sin^2alpha
c)2left(sinalpha-cosalpharight)^2-left(sinalpha+cosalpharight)^2+left(sinalpha.cosalpharight)
d)left(tanalpha-cotalpharight)^2-left(sinalpha+cotalpharight)^2
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Giúp mình vs chiều phải nộp bài rồi
a)C= \(4\cos^2\alpha-3\sin^2\alpha.cos=\frac{4}{7}\)
b)\(\cos^2\alpha+\cos^2\beta+\cos^2\alpha.\sin^2\beta+\sin^2\alpha\)
c)2\(\left(\sin\alpha-\cos\alpha\right)^2-\left(\sin\alpha+\cos\alpha\right)^2+\left(\sin\alpha.\cos\alpha\right)\)
d)\(\left(\tan\alpha-\cot\alpha\right)^2-\left(\sin\alpha+\cot\alpha\right)^2\)
Bạn không ghi rõ yêu cầu đề bài thì làm sao mà làm?
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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
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