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tuỳ ý giá trị biểu thức 
a, Ta có : \(\sin^2\alpha+\cos^2\alpha=1\)
Mà \(\sin^2\alpha=\cos^2\alpha\)
=> \(2\sin^2\alpha=1\)
=> \(\sin\alpha=\frac{1}{\sqrt{2}}\)
=> \(\alpha=45^o\)
b, Ta có : \(\tan\alpha.\cot\alpha=1\)
Mà \(\tan\alpha=\cot\alpha\)
=> \(\tan^2\alpha=1\)
=> \(\tan\alpha=1\)
=. \(\alpha=45^o\)
Vậy ...
a/ \(A=\frac{cot^2a-cos^2a}{cot^2a}-\frac{sina.cosa}{cota}\)
\(=\frac{\frac{cos^2a}{sin^2a}-cos^2a}{\frac{cos^2a}{sin^2a}}-\frac{sina.cosa}{\frac{cosa}{sina}}\)
\(=\left(1-sin^2a\right)-sin^2a=1\)
b/ \(B=\left(cosa-sina\right)^2+\left(cosa+sina\right)^2+cos^4a-sin^4a-2cos^2a\)
\(=cos^2a-2cosa.sina+sin^2a+cos^2a+2cosa.sina+sin^2a+\left(cos^2a+sin^2a\right)\left(cos^2a-sin^2a\right)-2cos^2a\)
\(=2+\left(cos^2a-sin^2a\right)-2cos^2a\)
\(=2-sin^2a-cos^2a=2-1=1\)
Câu 1:
Ta có: \(\cos\left(90^0-\alpha\right)=\sin\alpha\)
\(\Leftrightarrow\sin\alpha=1:\sqrt{\dfrac{1^2+2^2}{1}}=1:\sqrt{5}=\dfrac{\sqrt{5}}{5}\)
Câu 2:
a) \(\cos\alpha=\sqrt{1-\sin^2\alpha}=\sqrt{1-\dfrac{16}{25}}=\dfrac{3}{5}\)
\(\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=\dfrac{4}{5}:\dfrac{3}{5}=\dfrac{4}{3}\)
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
a) sin a < tan a
b) cos a < cot a
\(a.tan\alpha=\dfrac{sin\alpha}{cos\alpha}< sin\alpha\left(\alpha nhọn\Rightarrow sin\alpha>0,cos\alpha>0\right)\)
\(b.cot\alpha=\dfrac{cos\alpha}{sin\alpha}< cos\alpha\left(\alpha nhọn\Rightarrow sin\alpha>0,cos\alpha>0\right)\)
a)<
b)<
a) sin a < tan a
b) cos a < cot a
sin a < tan a
cos a > cot a
a) sin α < tan α
b) cos α > cot α
a, sin a < tan a
b, cos a > cot a
a) sin α< tan α
b) cos α> cot α
a) sin a< tan a
b) cos a > cot a
a) sin a < tan a
b) cos a > cot a
a, sin a < tan a
b, cos a > cot a
a) sin a < tan a
b) cos a > cot a
sin a < tan a
cos a > cot a
a) \sin \alpha < \tan \alphasinα<tanα;
b) \cos \alpha > \cot \alphacosα>cotα.
a,sin α <tan α
b,cos α>cot α
a) \sin \alpha < \tan \alphasinα<tanα
b) \cos \alpha > \cot \alphacosα>cotα
a) \sin \alpha < \tan \alphasin α < tan α
b) \cos \alpha > \cot \alphacos α > cot α.
sin a < tan a
cos a > cot a
a) sin α < tan α
b) cot α < cos α
a ) sin α ≤ tan α
b ) cos α ≥ cot α