Given (SiNx + cosx) / (SiNx cosx) = 2, then the value of sinxcosx is

Given (SiNx + cosx) / (SiNx cosx) = 2, then the value of sinxcosx is

(sinx+cosx)/(sinx-cosx)=2
sinx+cosx=2sinx-2cosx
-sinx=-3cosx
sinx=3cosx
Square gain
sin²x=9cos²x
So 10cos & # 178; X = 1
We get cos & # 178; X = 1 / 10
sin²x=9/10
therefore
(sinxcosx)²=9/100
Because SiNx = 3cosx is the same sign
So sinxcosx > 0
So sinxcosx = 3 / 10
If (2a + 1) and (2a-1) are reciprocal to each other, the value of real number a is a ± 1 B ± 1 / 2 C ± 2 / 2 root 2 D ± 1 or - 2
The root of C ± 2 is 2
（2a+1)(2a-1)=1
4a^2-1=1
a^2=1/2
A = ± 2 / 2 root sign 2
If (2a + 1) and (2a-1) are reciprocal, then (2a + 1) × (2a-1) = 1
That is, 4A ^ 2 - 1 = 1
C
（2a+1）*（2a-1）=1
a^2=1/2
sinxcosx=3/8 π/4
(cosx-sinx)^2
=cos^2(x)+sin^2(x)-2sinxcosx
=1-2*3/8
=1/4
|cosx-sinx|=1/2
Cosx SiNx = 1 / 2 or - 1 / 2
A is a real number, and the square of a plus B is equal to the minimum of the square of 1,2a plus the square of 7b
a+b^2=1
2a^2+7b^2
=2a^2+7(1-a)
=2a^2-7a+7
=2(a-7/4)^2+7-49/8
That is, when a = 7 / 4, the original formula has the minimum value, which is 7-49 / 8 = 7 / 8
a+b^2=1
2a^2+7b^2
=2a^2+7(1-a)
=2a^2-7a+7
=2(a-7/4)^2+7-49/8
That is, when a = 7 / 4, the original formula has the minimum value, which is 7-49 / 8 = 7 / 8
a+b^2=1
b^2=1-a
Then: 2A ^ 2 + 7b ^ 2
=2a^2+7(1-a)^2
=2a^2+7(1-2a+a^2)
=9a^2-14a+7
When a = 0, 2A ^ 2 + 7b ^ 2 has the minimum value, 2A ^ 2 + 7b ^ 2 = 7.
Two
Given SiNx = 1 / 8 and 0 ° < x < 45 °, find the value of cosx SiNx
If x is an acute angle, cosx > 0
Because Sin & # 178; X + cos & # 178; X = 1
So cosx = 3 √ 7 / 8
So the original formula = (3 √ 7-1) / 8
cos²x=1-sin²x=1-1/64=63/64
∵0°＜x＜45°
∴cosx=3√7/8
cosx-sinx=(3√7-1)/8
It is calculated by the formula SiNx square + cosx square = 1
Square of 1 / 64 + cosx = 1
Cosx = positive and negative (3 √ 7-1) / 8
In the first quadrant, so it's positive
If the square root of a positive real number is a + 1 and 2A + 5, then the positive real number is equal to 3Q
The result of square root is a pair of opposite numbers, that is, a + 1 = - (2a + 5). Solving the equation, we get a = - 2, that is, the square root of positive real number is - 1 and 1, and the positive real number is 1
Given that the function y = SiNx + α cosx is symmetric with respect to x = π / 8, then the value of α——
Because 0 and π / 4 are symmetric points about x = π / 8
The function y = SiNx + α cosx is symmetric with respect to x = π / 8
So f (0) = f (π / 4)
a=√2/2+√2/2*a
2a=√2/+√2*a
The solution is: a = √ 2 + 1
Function y = SiNx + α cosx = √ (1 + α ^ 2) sin (x + a), where cosa = 1 / √ (1 + α ^ 2)
The graph is symmetric about x = π / 8
Then when x = π / 8, the function gets the maximum value
That is, π / 8 + a = π / 2 + K π, K ∈ Z
A=kπ+3π/8
Then cosa = cos (K π + 3 π / 8) = cos3 π / 8 = 1 / √ (1 + α ^ 2) then 1 / (1 + α ^ 2) = cos ^ 2 (3 π / 8)
If a is known to be a real number and a ≠ 0, then a is opposite to it, and the sum of the three reciprocal numbers is___ The product is___ ?
Then a and its opposite number, the sum of the three reciprocal numbers is_ 1/A__ The product is_ -A__
If a is known to be a real number and a ≠ 0, then a is opposite to it, and the sum of the three reciprocal numbers is_ 1/A__ The product is_ -A__ ?
A+(-A)+(1/A)=1/A
A*(-A)*(1/A)=-A
(SiNx + cosx) / (SiNx cosx) = 2, find the value of sinxcosx
sinx+cosx=2sinx-2cosx sinx=3cosx
sin^2x+cos^2x=1 10cos^2x=1
sinx*cosx=3cos^2x=3/10
Thank you
Whether the reciprocal of real number a is 1 / A, urgent~~~~~~~~~~
Not necessarily. If a is 0, there is no countdown
yes!
Not necessarily, except 0.