Ta có: \(\left(\sin\alpha+\cos\alpha\right)^2=\sin^2\alpha+\cos^2\alpha+2\sin\alpha.\cos\alpha\)\(=1+2.\frac{1}{2}=1+1=2\)

=> \(\sin\alpha+\cos\alpha=\sqrt{2}\)=> \(\sin\alpha=\sqrt{2}-\cos\alpha\)

=> \(\sin\alpha.\cos\alpha=\left(\sqrt{2}-\cos\alpha\right).\cos\alpha=\sqrt{2}.\cos\alpha-\cos^2\alpha=\frac{1}{2}\)

=> \(\cos^2\alpha-\sqrt{2}\cos\alpha+\frac{1}{2}=0\)

Xong bạn giải phương trình bậc 2 => \(\cos\alpha=\frac{\sqrt{2}}{2}\)=> \(\alpha=45^o\)

hi hoi me chi i

con gái hả?

Ta thấy :\(x^2-2x+5=x^2-2x+1+4\)

\(=\left(x-1\right)^2+4\ge4\forall x\)

\(\Rightarrow\sqrt{x^2-2x+5}\ge\sqrt{4}=2\)

\(\Rightarrow\frac{1}{\sqrt{x^2-2x+5}}\le2\)

Xảy ra khi \(x=1\)

ukm,mik ko phải fan của linh kaa cũng ko phải antifan của cô ta

bn bị sao vậy???

chào cỏ

a, \(2\sqrt{3}-\sqrt{27}+\sqrt{75}=6,92820323\)

a) \(2\sqrt{3}-\sqrt{27}+\sqrt{75}\)

\(=2\sqrt{3}-3\sqrt{3}+5\sqrt{3}\)

\(=\sqrt{3}\left(2-3+5\right)\)

\(=4\sqrt{3}\)

b)\(\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{4+2\sqrt{3}}\)

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

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

\(=2\)

\(a,ĐKXĐ:\hept{\begin{cases}a>0\\a\ne1\end{cases}}\)

\(b,A=\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)\left(\frac{a-\sqrt{a}}{\sqrt{a}+1}-\frac{a+\sqrt{a}}{\sqrt{a}-1}\right)\)

\(=\frac{a-1}{2\sqrt{a}}.\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}+1}-\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}-1}\right)\)

\(=\frac{a-1}{2\sqrt{a}}.\frac{\sqrt{a}.\left(\sqrt{a}-1\right)^2-\sqrt{a}\left(\sqrt{a}+1\right)^2}{a-1}\)

\(=\frac{\sqrt{a}\left(\left(\sqrt{a}-1\right)^2-\left(\sqrt{a}+1\right)^2\right)}{2\sqrt{a}}\)

\(=\frac{\sqrt{a}.\left(\sqrt{a}-1-\sqrt{a}-1\right).\left(\sqrt{a}-1+\sqrt{a}+1\right)}{2\sqrt{a}}\)

\(=\frac{\sqrt{a}.\left(-2\right).2\sqrt{a}}{2\sqrt{a}}\)

\(=-2\sqrt{a}\)

\(c,\)Để A= -4 thì 

\(-2\sqrt{a}=-4\Leftrightarrow\sqrt{a}=2\Leftrightarrow a=4\)

Kết bạn với mình nha ....

NX \(A=\sqrt{1+\frac{1}{a^2}+\frac{1}{\left(a+1\right)^2}}\)

\(A^2=1+\frac{1}{a^2}+\frac{1}{\left(a+1\right)^2}=\frac{a^2\left(a+1\right)^2+\left(a+1\right)^2+a^2}{a^2\left(a+1\right)^2}\)

\(=\frac{a^2\left(a^2+2a+1+1\right)+\left(a+1\right)^2}{a^2\left(a+1\right)^2}\)=\(\frac{a^4+2a^3+2a^2+\left(a+1\right)^2}{a^2\left(a+1\right)^2}\)

\(=\frac{a^4+2a^2\left(a+1\right)+\left(a+1\right)^2}{a^2\left(a+1\right)^2}=\frac{\left(a^2+a+1\right)^2}{a^2\left(a+1\right)^2}\)=\(\left[\frac{a^2+a+1}{a\left(a+1\right)}\right]^2\)suy ra A=\(\frac{a^2+a+1}{a\left(a+1\right)}\)

                                                                                                =\(\frac{a\left(a+1\right)+1}{a\left(a+1\right)}=1+\frac{1}{a\left(a+1\right)}=1+\frac{1}{a}-\frac{1}{a+1}\)

ap dung vao bai ta co =\(\left(1+\frac{1}{2}-\frac{1}{3}\right)+\left(1+\frac{1}{3}-\frac{1}{4}\right)+...+\left(1+\frac{1}{2012}-\frac{1}{2013}\right)\)

=\(2011+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2012}-\frac{1}{2013}\right)\)= \(2011+\frac{1}{2}-\frac{1}{2013}=2011,499503\)