The minimum positive period of y = radical (cosx ^ 2-cosx ^ 4) is

The minimum positive period of y = radical (cosx ^ 2-cosx ^ 4) is

y=√(cosx^2-cosx^4)
=√[cosx^2(1-cosx^2)]
=√[cosx^2*sinx^2)]
=√[4cosx^2*sinx^2)/4]
=√[(sin2x^2)/4]
=∣sin2x∣/2
T=2π/2=π

Finding the minimum positive period sum of COS ^ 2x-sin2x + radical 3 (2sinx * cosx)
Finding the minimum positive period and range of COS ^ 2x-sin2x + radical 3 (2sinx * cosx)

Cos ^ 2x-sin2x + radical 3 (2sinx * cosx)
=(1 + cos2x) / 2-sin2x + radical 3sin2x
=[(radical 3-1) sin2x + (1 / 2) cos2x] + 1 / 2
=[(17-8 radical 3) / 4] * sin (2x + W) + 1 / 2
(here tanw = 1 / [2 (radical 3-1)])
Then: the minimum positive period T = 2pi / 2 = Pi
Because: sin (2x + W) belongs to [- 1,1]
Then: [(17-8 radical 3) / 4] sin (2x + W)
Belonging to: [(8 radical 3-17) / 4, (17-8 radical 3) / 4]
Then cos ^ 2x-sin2x + radical 3 (2sinx * cosx)
=[(17-8 radical 3) / 4] * sin (2x + W) + 1 / 2
Belonging to: [(8 radical 3-15) / 4, (19-8 radical 3) / 4]

If f (x) = root 3sinx + cosx, find the minimum positive period and the maximum. If f (a) = 2 / 3, find the value of COS (2a + Pai / 3)

F (x) = root 3sinx + cosx = 2 (√ 3 / 2sinx + 1 / 2cosx) = 2 (sinxcos π / 6 + cosxsin π / 6) = 2Sin (x + π / 6), so the minimum positive period of the function is 2 π; the maximum value is 2F (a) = 2Sin (a + π / 6) = 2 / 3sin (a + π / 6) = 1 / 3cos (2a + π / 3) = cos [2 (a + π / 6)] = 1-2sin & # 178; (a + π / 6)

Given the function f (x) = [cos ^ 3 (x + π) / 2 * cosx / 2] / TaNx, (1) find the domain of definition of F (x), (2) judge the parity of F (x)

1. Denominator cannot be 0, TaNx ≠ 0
The domain of definition (- π / 2 + K π, + K π) and (K π, π / 2 + K π), K ∈ Z
There is an intersection between the range of X in TaNx and the range of X that makes TaNx ≠ 0
2. Need to simplify
f(x)=[cos^3(x+π)/2*cosx/2]/tanx
=[cos^3(x/2+π/2)*cos(x/2)]/(sinx/cosx)
=-sin^3(x/2)*cos(x/2)*cosx/[2sin(x/2)*cos(x/2)]
=-1/2sin^2(x/2)*cosx
That's all it takes to simplify
f(-x)=-1/2sin^2(-x/2)*cos(-x)
=-1/2sin^2(x/2)*cosx
=f(x)
F (x) even function
If you don't understand this question, you can ask,

Finding the period of function y = cosx (1 + cosx) TaNx / 2
The answer is 2 π, but there is a strange place. Finally, it turns to y = 1 / 2 sin2x, but the answer says that the original function requires x ≠ 2K π, but for TaNx / 2, shouldn't x ≠ K π

y=0.5sin2x
so:
Cosx / 2 cannot be equal to 0
X / 2 cannot be equal to K π
therefore
x≠2kπ
Do a topic to think clearly, basic things

Intelligence arithmetic problems (can measure your good learning in that period)
Five five equals 24
Now I know the answer of a middle school: (5-5 / 5 / 5) * 5 = 24
5 * 5 - (5-5 power of 5) = 0
Seeking

The answer you said in middle school should be that in primary school
The primary school answer is: (5-5 / 5 / 5) * 5 = 24
The answer of middle school is: the (5-5) power of 5 * 5-5 = 24
High school answer is: 5! / 5 - (5! - 5!) * 5!

I didn't understand the arithmetic problem of intelligence test,
I can't do five arithmetic questions. What's the answer,
Question 1
1 & nbsp; & nbsp; 3 & nbsp; & nbsp; 2 & nbsp; & nbsp; 4 & nbsp; & nbsp; 6 & nbsp; & nbsp; 5 & nbsp; & nbsp; 7 & nbsp; (& nbsp;), (& nbsp;) what are the numbers in?
The options are & nbsp; 8 & nbsp; & nbsp; 9 & nbsp; & nbsp; & nbsp; 10 & nbsp; & nbsp; & nbsp; 11 & nbsp; & nbsp; 12 & nbsp; & nbsp; 13
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Question 2
961 & nbsp; & nbsp; (25) & nbsp; & nbsp; 432 & nbsp; 932 & nbsp; & nbsp; (& nbsp;) & nbsp; 731 & nbsp;, & nbsp; (& nbsp;) what are the numbers in it?
The options are & nbsp; 46 & nbsp; & nbsp; 36 & nbsp; & nbsp; 42 & nbsp; & nbsp; 38 & nbsp; & nbsp; & nbsp; 64 & nbsp; & nbsp; & nbsp; 188
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Question 3
What are the numbers in 1 & nbsp; & nbsp; 8 & nbsp; & nbsp; 27 & nbsp; (& nbsp;), & nbsp; (& nbsp;)?
The options are & nbsp; & nbsp; 64 & nbsp; & nbsp; 48 & nbsp; & nbsp; & nbsp; 56 & nbsp; & nbsp; & nbsp; 128 & nbsp; & nbsp; & nbsp; 96 & nbsp; & nbsp; & nbsp; & nbsp; 35
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Question 4
16 （96） 12  10  （ ） 7.5
The options are & nbsp; & nbsp; & nbsp; & nbsp; 60 & nbsp; & nbsp; & nbsp; 70 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 50 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 40 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 100 & nbsp; & nbsp; & nbsp; & nbsp; & 80 & nbsp; & nbsp;
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Question 5
41  （28）  27  83  （ ）  65
The options are & nbsp; & nbsp; & nbsp; 24 & nbsp; & nbsp; & nbsp; 26 & nbsp; & nbsp; & nbsp; 20 & nbsp; & nbsp; & nbsp; 38 & nbsp; & nbsp; & nbsp; & nbsp; 36 & nbsp; & nbsp; & nbsp; & nbsp; 42
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The rule of 1.9 is + 2-1 + 2 + 2-1 + 2 + X. the most likely x is 2, so the answer is 7 + 2 = 9
2.36 this question you can know in Baidu search, there are detailed answers, I will not repeat here. Some people think that the answer to this question can also be 25, that is to add all the numbers, I think it can
3.64 this problem is relatively simple, the rule is that the third power of n is 1, the third power of 2 is 8, the third power of 3 is 27, then the third power of 4, the answer is 64
4. The answer to this question is more than one. If you choose 60 according to your answer, the method is right. The least common multiple of the left and right numbers * 2.16 and 12 is 48, so 48 * 2 = 96 in brackets, so the answer can be deduced that the least common multiple of 10 and 7.5 is 30, so the answer is 30 * 2 = 60
But I think it's OK to multiply the left and right numbers and divide them by 2. If so, the answer is 7.5 * 10 / 2 = 37.5
5. This problem is easier to solve. The answer is 36. The difference between the left and right numbers * 2 is OK. There is no other answer

An arithmetic problem
If:
1=5
2=15
3=215
4=2145
5=?

5=1

An IQ arithmetic problem
A child spent 80 yuan to buy three fish, and then three old men each spent 30 yuan to buy fish, so the child had 99 yuan in hand. After returning home, the child's mother said how to earn other people's money, and asked the child to return the money. The child returned 2 yuan to each old man, a total of 6 yuan, leaving 4 yuan for the child to buy sugar. But each old man actually spent 28 yuan, 28 * 3 = 84 yuan, plus 4 yuan to buy sugar, It's 88 yuan in total. Why is it two yuan less? Where's the two yuan?
Is the two yuan for the children or the three old men?

But each old man actually spent 28 yuan, 28 * 3 = 84 yuan, plus 4 yuan to buy sugar, here is the trap ~ 84 yuan is Xiaoming's 90 yuan, also 6 yuan later bought sugar, so Xiaoming finally 80 yuan, buy sugar that 4 yuan is equivalent to the old man to pay, is 84 (old man pay) - 4 (buy sugar) = 80, you can also think so, at the beginning

Algebra and arithmetic
Given that the rational number x satisfies 4x & sup2; - 4x + 1 = 0, then the value of the algebraic formula 2x + X / 2 is

4x²-4x+1=0
x=1/2
2x+x/2=1+1/4=1.25