\(\cos^225^0-\cos^235^0+\cos^245^0-\cos^255^0+\cos^265^0\)

\(=1-1+\dfrac{1}{2}=\dfrac{1}{2}\)

Bài 48:

1/ 17(-84) + 17(-16) = 17 \(\left[\left(-84\right)+\left(-16\right)\right]\) = 17. (-100) = -1700

2/ 15.58 - 15.48 = 15.(58 - 48) = 15 . 10 = 150

3/ -37.86 + 37.76 = 37 .(-86 + 76) = 37. (-10) = -370

4/ 1975 .(-115) + 1975.15 = 1975. (-115 + 15) = 1975 . (-100) = -197500

5/ 79.89 - 79.(-11) = 79. (89 + 11) = 79 . 100 = 7900

6/ 48.195 - 48 . 95 = 48. (195 - 95) = 48 . 100 = 4800

7/ 157.17 - 157.7 = 157. (17 - 7) = 157 . 10 = 1570

8/ 15(-176) + 15.76 = 15. (-176 + 6) = 15 . 100 = 1500

9/ 47.(-147) - 47 .(-47)= 47 (-147 + 47) = 47. (-100) = -4700

10/ 153.177 - 153.77 = 153. (177 - 77) = 153. 100 = 15300

11/ 15. (4 - 7) - 15. (5 - 3)

= 15. (-3) - 15. 2

= 15. (-3 - 2)

= 15. (-5)

= -75

12/ 73. (8 - 59) - 59. (8 - 73)

= 73. 8 - 73. 59 - 59. 8 + 73. 59

= 8. (73 - 59) + 73. (59 - 59)

= 8. (73 - 59) + 0

= 8. 14

= 112

13/ 159. (18 - 59) - 59. (18 - 159)

= 159. 18 - 159. 59 - 59. 18 + 59. 159

= 18.(159 - 59) - 59. (159 - 159)

=  18.(159 - 59) - 0 

= 18. 100

= 1800

14/ -145. (13 - 57) + 57. (10 - 145)

= -145. 13 + 145. 57 + 57. 10 - 57. 145

= -145. 13 + 57. 10

= -1885 + 570

= 2455

Những câu còn lại tương tự

Bài 16: 

a: Ta có: \(P=\left(\dfrac{\sqrt{a}+1}{\sqrt{ab}+1}+\dfrac{\sqrt{ab}+\sqrt{a}}{\sqrt{ab}-1}-1\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{ab}+1}-\dfrac{\sqrt{ab}+\sqrt{a}}{\sqrt{ab}-1}+1\right)\)

\(=\dfrac{a\sqrt{b}-\sqrt{a}+\sqrt{ab}-1+ab+\sqrt{ab}+a\sqrt{b}+\sqrt{a}-ab+1}{\left(\sqrt{ab}+1\right)\left(\sqrt{ab}-1\right)}:\dfrac{a\sqrt{b}-\sqrt{a}+\sqrt{ab}-1-ab-\sqrt{ab}-a\sqrt{b}-\sqrt{a}+ab-1}{\left(\sqrt{ab}+1\right)\left(\sqrt{ab}-1\right)}\)

\(=\dfrac{2a\sqrt{b}+2\sqrt{ab}}{-2\sqrt{a}-2}\)

\(=\dfrac{2\sqrt{ab}\left(\sqrt{a}+1\right)}{-2\left(\sqrt{a}+1\right)}\)

\(=-\sqrt{ab}\)

Câu 5:

\(\dfrac{x}{y}=a\Rightarrow\dfrac{x}{a}=\dfrac{y}{1}=\dfrac{x-y}{a-1}=\dfrac{x+y}{a+1}\)

\(\Rightarrow\dfrac{x+y}{x-y}=\dfrac{a+1}{a-1}\)

Câu 6:

\(9x=5y\Rightarrow\dfrac{x}{5}=\dfrac{y}{9}\)

\(\Rightarrow\dfrac{x}{5}=\dfrac{y}{9}=\dfrac{3x}{15}=\dfrac{2y}{18}=\dfrac{3x-2y}{15-18}=\dfrac{12}{-3}=-4\)

\(\Rightarrow\left\{{}\begin{matrix}x=\left(-4\right).5=-20\\y=\left(-4\right).9=-36\end{matrix}\right.\)

Câu 7:

\(\dfrac{x}{-5}=\dfrac{y}{7}=\dfrac{x+y}{-5+7}=\dfrac{-10}{2}=-5\)

\(\Rightarrow\left\{{}\begin{matrix}x=\left(-5\right).\left(-5\right)=25\\y=\left(-5\right).7=-35\end{matrix}\right.\)

XXét tứ giác AMDN có ^AMD=^MAN=^AND=90∞

⇒AMDN là hình chữ nhật

hcn AMDN có AD là phân giác góc A

⇒AMDN là hình vuông(dấu hiệu 3)