(2012 the second mock exam of Pudong New Area) the known function f (x) =2sinxcosx+2cos2x. (1) asks for the monotonous increasing interval of function f (x); (2) after the function y=f (x) image is shifted to 4 units of the right, we get the image of function y=g (x) and find the solution of equation g (x).

(1) The function f (x) of the function f (x) is the function f (x) = 2 SiNx cosx x + 2cos2x = 2x + cos2x + 1 = 2 sin (2x + π 4) + 1, and by 2K π - π (2k π - π 2 ≤ 2x + π 4 ≤ 2K π + π 4 ≤ 2K + π 2 (K ∈ z) we get: K π - 3 π 8 ≤ 3 π 8 ≤ x ≤ K π + π + π 8 (K ∈ z), then the monotone increasing interval of F (x) is [K π π - 3 π 3 π 8, π 8, K π 8, K π + π + 8] (K \\\\\\\\\\\\\\sin (2x - π 4) = 0,  2x- If π 4 = k π (K ∈ z), then x = k π 2 + π 8 (K ∈ z)

How to find 2cos ^ 215 ° - 1

Double angle theorem
2cos^2 15°-1=cos30°=√3/2

If Tan α = - 2, find 1 / 4 sin α squared + 2 / 5 cos α squared

7/25
Using the homogeneous cut method, first divide the original formula by 1, 1 into sin square @ + cos square @, and then divide the semicolon up and down by cos square @. Ah, it's too hard for my mobile phone to type these symbols

(1)2（a^2-ab)-2a^2+3ab (2)5(2x-7y)-3(4x-10y) (3)(x+y)-[3x+(-x+y)]

2（a^2-ab)-2a^2+3ab =2a²-2ab-2a²+3ab=ab
5(2x-7y)-3(4x-10y)=10x-35y-12x+30y=-2x-5y
(x+y)-[3x+(-x+y)] =x+y-3x-(-x+y)=-2x+y+x-y=-x

Li Hong read 150 pages of a story book of 200 pages. Li Hong read ()% of the whole book, and there are ()% left. The number of pages she read is ()%, and the number of pages she didn't read is ()%. The number of pages she read is () more than that of the whole book, and () less than that of the whole book

Li Hong read 150 pages of a story book of 200 pages. Li Hong read (75)% of the whole book and (25)% left. The number of pages she didn't read was (300)%, and the number of pages she didn't read was (33.3)%. The number of pages she read was (200)%, and the number of pages she didn't read was (67)%

If the circumference of an isosceles triangle is 20cm and one side is 2cm, the waist length of an isosceles triangle is () cm

If the circumference of an isosceles triangle is 20 cm and one side is 2 cm, the waist length of an isosceles triangle is (9) cm
If this side is the waist, then the bottom edge = 20-2-2 = 16 cm; 16 > 2 + 2; does not conform to the requirements;
Waist = (20-2) △ 2 = 9cm

A car from a to B, 4 hours line one tenth of the whole, 8 hours line a few parts of the whole? There are still a few parts of the line?

1/10*8/4＝2/10＝1/5
And 1-1 / 5-1 / 10 = 7 / 10

Rational number is divided into positive rational number, negative rational number and zero. A is known to be rational number. Try to explore the size of a and half a

I'll give you a way to compare the size
Theoretical basis: if A-B > 0, then a > b;
If A-B < 0, then a < B;
If A-B = 0, then a = B
So, A-A / 2 = A / 2
(1) When a = 0, a / 2 = 0, a = A / 2
(2) When a > 0, a / 2 > 0, then a > A / 2
(3) When a < 0, a / 2 < 0, then a < A / 2
The method of making difference is very useful in comparing the size. Its idea is to deal with complex structures. By making the difference into several factors to multiply and divide, we can judge the positive and negative one by one, and finally get a total positive and negative, so as to compare the size relationship of two quantities

The maximum acceleration of a fighter on an aircraft carrier during takeoff is a = 9m / S2, and the aircraft can only take off when its speed reaches 60m / s
X = 0.5at square 72 = 4.5t square t = 4S v = at = 9 * 4 = 36m / s 60-36 = 24
The speed of aircraft carrier shall not be less than 24m / s
T = 4S why?
If the runway of the aircraft carrier is 72m, how fast should the aircraft carrier advance at a constant speed? Sorry, half of the question

Take off speed of fighter (i.e. speed of fighter relative to ground) = = speed of aircraft carrier relative to ground plus speed of fighter relative to aircraft carrier x = 0.5at square 72 = 4.5t square t = 4S v = at = 9 * 4 = 36m / s. These three formulas are all calculated with aircraft carrier as reference, so 36 is the maximum speed of fighter relative to aircraft carrier, The take-off speed of the fighter (that is, the speed of the fighter relative to the ground) is 60, and the running speed of the aircraft carrier is the speed of the aircraft carrier relative to the ground = = 60-36 = = 24
72 = 4.5t square to get the kinematics formula of T = 4S

How to solve the equation that one half plus x equals five sixths?

1/2 + x = 5/6
x = 5/6 - 1/2
x = 5/6 - 3/6
x = 2/6
X = 1 / 3 (1 / 3)