Cho a,b∈R;n∈N∗" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvetica,arial,sans-serif; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a,b∈R;n∈N∗${\displaystyle a,b\in R;n\in N^{\ast }}$. Chứng minh rằng:

Cho tam giác ABC có A^=900" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">ˆA=900$\hat{A}={90}^0$;B^=450" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">ˆB=450$\hat{B}={45}^0$,Vẽ tia phân giác AD.Trên tia đối của tia AD lấy điểm E sao cho AE=BC.Trên tia đối của tia CA lấy điểm F sao cho CF=AB.CMR: BE=BF và BE⊥BF

Chứng minh rằng với mọi số nguyên dương k" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">k${\displaystyle k}$ ; ta có đẳng thức :

$$\frac{1}{{\sin }^2\frac{\pi }{4k+2}}+\frac{1}{{\sin }^2\frac{3\pi }{4k+2}}+\frac{1}{{\sin }^2\frac{5\pi }{4k+2}}+\cdots +\frac{1}{{\sin }^2\frac{(2k-1)\pi }{4k+2}}=2k(k+1$$ 

Cho tam giác $ABC$ có B^=C^=50∘" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">ˆA=ˆB=60∘$\hat{B}=\hat{C}={50}^{\circ }$. Gọi tia Cx$Am$ là tia phân giác của góc ngoài ở đỉnh $C.$ Hãy chứng tỏ //BC" role="presentation" style="border:0px; direction:ltr; display:inline-table; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">AB//Cx$Am//BC$.

Cho tam giác $ABC$ có B^=C^" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">ˆB=ˆC$\hat{B}=\hat{C}$. Tia phân giác góc $A$ cắt $BC$ tại $D.$ Chứng minh rằng $DB=DC,AB=AC.$

Cho tam giác $ABC$ có B^=C^=50∘" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">ˆA=ˆB=60∘$\hat{B}=\hat{C}={50}^{\circ }$. Gọi tia $Am$ là tia phân giác của góc ngoài ở đỉnh $\mathrm{C.}$ Hãy chứng tỏ //BC" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">Cx/
/AB.

Cho tam giác ABC, AB < AC, AB = BC và ABC&#x005E;=80o" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">ˆABC=80o$\widehat{ABC}={80}^o$. Điểm I nằm trong &#x0394;ABC" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">ΔABC$\mathrm{\Delta }ABC$ sao cho AIC&#x005E;=10o" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">ˆAIC=10o$\widehat{AIC}={10}^o$ và ICA&#x005E;=30o" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">ˆICA=30o$\widehat{ICA}={30}^o$. Tính AIB&#x005E;" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">ˆAIB

Cho hình 56, trong đó //HK,AH//BK." role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">AB//HK,AH//BK.$AB//HK,AH//BK.$ Chứng minh rằng $AB=HK,AH=BK.$

So sánh \(A=\frac{2^{2016}+7}{2^{2014}+7}\)và \(B=\frac{2^{2013}+1}{2^{2011}+1}\)