Với giả thiết biểu thức có nghĩa hãy rút gọn: \(A=\frac{\cos7x-\cos8x-\cos9x+\cos10x}{\sin7x-\sin8x-\sin9x+\sin10x}\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
T
19 tháng 5 2019
Em có cách này,anh check lại nhé!
Theo nguyên lí Dirichlet,trong ba số (a - 1) ; (b - 1); (c - 1) tồn tại hai số có tích không âm.
Không mất tính tổng quát,giả sử \(\left(a-1\right)\left(b-1\right)\ge0\Rightarrow ab\ge a+b-1\)
\(\Rightarrow abc\ge ac+bc-c\)
Suy ra \(VT\ge a^2+b^2+\left(c^2+ac+bc-c\right)\)
\(=a^2+b^2+c\left(a+b+c-1\right)=a^2+b^2+2c\)
Ta cần chứng minh \(a^2+b^2+2c\ge4\)
Thật vậy,BĐT \(\Leftrightarrow\left(a^2+1\right)+\left(b^2+1\right)+2c\ge6\)
Áp dụng BĐT Cô si (AM-GM) ta được: \(VT\ge2\left(a+b+c\right)=2.3=6\)(Q.E.D)
KN
17 tháng 5 2019
1 the aim of the culture festival is ....... friendship between the two countries
A . promote B . promoting C . to promote D. being promoted
2. people he ......... turned out to be only fair - weather friends
A. trusted B. has trusted C was trusting D had trusted
3. How can you let such a silly incident ............ your friendship
A. wreck B to wreck C wrecking D that wrecks
4. it has become necessary ....... water in the metropolitan area because of the severe drought
A. rationing B ration C to ration D to have rationed
5 All the pasengers were made.............. their seat belts during the turbulence
A. buckle B to buckle C buckling D for buckling
6. .......... good ice cream , you need to use a lot of cream
A Make B making C to make D for make
7 , i got my friend ........... her car for the weekend
A . to let me to borrow B to let me borrow C let me borrow D let me to borrow
8 they .......... good friends , but they have fallen out recently
A . used to be B would be C were D are
16 tháng 5 2019
chịuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu
máy tính tui ko ghi het dc
16 tháng 5 2019
4 nhe bạn mình cũng ko chắc đâu nên bạn tự tìm hiểu nhé
\(A=\frac{cos7x-cos8x-cos9x+cos10x}{sin7x-sin8x-sin9x+sin10x}=\frac{(cos10x+cos7x)-\left(cos9x+cos8x\right)}{\left(sin10x+sin7x\right)-\left(sin9x+sin8x\right)}.\)
\(=\frac{2cos\frac{17x}{2}cos\frac{3x}{2}-2cos\frac{17x}{2}cos\frac{x}{2}}{2sin\frac{17x}{2}cos\frac{3x}{2}-2sin\frac{17x}{2}cos\frac{x}{2}}=\frac{2cos\frac{17x}{2}\left(cos\frac{3x}{2}-cos\frac{x}{2}\right)}{2sin\frac{17x}{2}\left(cos\frac{3x}{2}-cos\frac{x}{2}\right)}=cotan\frac{17x}{2}.\)