b)\(\frac{\sqrt{27}}{\sqrt{12}}+\frac{1}{2}\)

\(=\frac{\sqrt{3}.\sqrt{9}}{\sqrt{3}.\sqrt{4}}+\frac{1}{2}\)

\(=\frac{\sqrt{9}}{\sqrt{4}}+\frac{1}{2}\)

\(=\frac{3}{2}+\frac{1}{2}\)

\(\frac{4}{2}=2\)

a) \(\sqrt{45}.\sqrt{15}.\sqrt{27}\)

\(=\left(\sqrt{15}\right)^2.\left(\sqrt{3}\right)^2.\sqrt{9}\)

\(=15.3.3\)

\(=135\)

2

\(\sqrt{12}-\sqrt{27}+\sqrt{3}\)

\(=\sqrt{3}\left(\sqrt{4}-\sqrt{9}+\sqrt{1}\right)\)

\(=\sqrt{3}\left(2-3+1\right)\)

\(=\sqrt{3}.0=0\)

\(\sqrt{12}\)-  \(\sqrt{27}\)+ \(\sqrt{3}\)

= \(2\sqrt{3}\)- \(3\sqrt{3}\)+ \(\sqrt{3}\)

= 0

#mã mã#

a, \(\sin25^0\)< \(\sin70^0\)

b, \(\cos40^0\)> \(\cos75^0\)

c, \(\sin35^0\)= \(\cos55^0\)

\(\cos55^0\)< \(\cos35^0\)

\(\Rightarrow\)\(\sin35^0\)< \(\cos35^0\)

#mã mã#

a, ta có \(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}\)

                  \(\frac{1}{3}\)= \(\frac{\sin\alpha}{\cos\alpha}\)

                    \(\cos\alpha\)= 3 \(\sin\alpha\)

ta có \(\frac{\cos\alpha+\sin\alpha}{\cos\alpha-\sin\alpha}\)= \(\frac{3\sin\alpha+\sin\alpha}{3\sin\alpha-\sin\alpha}\)= \(\frac{4\sin\alpha}{2\sin\alpha}\)= \(2\)

#mã mã#

a, ta có \(\cos^2\alpha\)+  \(\sin^2\alpha\)= 1

                  1/5 + \(\cos^2\alpha\)= 1

                               \(\cos^2\alpha\)= 4/5

\(4\cos^2\alpha\)+6 \(\sin^2\alpha\)= 4 . 4/5 + 6.1/5=22/5

b, \(\sin\alpha\)= 2/3 

\(\sin^2\alpha\)= 4/9

\(\cos^2\alpha=\frac{5}{9}\)

\(5\cos^2\alpha+2\sin^2=\frac{5.5}{9}+\frac{2.4}{9}=\frac{33}{9}\)

#mã mã#

a, = \(\sin^2\alpha+2\sin\alpha.\cos\alpha+\cos^2\alpha\)+ \(\sin^2\alpha-2\sin\alpha\cos\alpha+\cos^2\alpha\)

= \(2\sin^2\alpha+2\cos^2\alpha\)= 4

b,=\(\sin\alpha\cos\alpha\)(\(\frac{\sin\alpha}{\cos\alpha}+\frac{\cos\alpha}{\sin\alpha}\))

= \(\sin\alpha\cos\alpha.\frac{\sin^2\alpha+\cos^2\alpha}{\sin\alpha\cos\alpha}\)

=1

#mã mã#

b, =1 

mk viết thiếu

#mã mã#