If SiNx + siny + Sinz = 0, cosx + cosy + cosz = 0, then cos (X-Y)=______ We need to explain it in detail

If SiNx + siny + Sinz = 0, cosx + cosy + cosz = 0, then cos (X-Y)=______ We need to explain it in detail

SiNx + siny = - sinzcosx + cosy = - cosz square sum Sin & sup2; X + cos & sup2; X + Sin & sup2; y + cos & sup2; y + 2 (cosx + cosy + sinxsiny) = Sin & sup2; Z + cos & sup2; Z1 + 1 + 2cos (X-Y) = 1, so cos (X-Y) = - 1 / 2
It is known that y = (M + 1) x + 2m square + 5m - 3 is a positive proportion function, and the proportion coefficient of this positive proportion function is obtained
y=(m+1)x+2m²+5m-3
Positive scaling function (K ＞ 0)
That is m + 1 = K
2m²+5m-3=0
(m+3)(2m-1)=0
m=-3 m=1/2
K = - 2 or 1.5
Because k > 0, k = 1.5
One point five
Y = (M + 1) x + 2m square + 5m-3
Positive scale function y = kx
That is m + 1 = K
2m square + 5m-3 = 0
(m+3)(2m-1)=0
m=-3 m=1/2
K = - 2 or 1.5
SiNx + siny + Sinz = 0; cosx + cosy + cosz = 0; find cos (X-Y)
SiNx + siny = - sinzcosx + cosy = - cosz square sum Sin & sup2; X + cos & sup2; X + Sin & sup2; y + cos & sup2; y + 2 (cosx + cosy + sinxsiny) = Sin & sup2; Z + cos & sup2; Z1 + 1 + 2cos (X-Y) = 1, so cos (X-Y) = - 1 / 2
If y = (n-2) times the absolute value of n of x minus one, then n is a positive proportional function=____
If y = (n-2) x ^ (| n | - 1) is a positive proportional function, then | n | - 1 = 1, and n-2 does not = 0
That is, n = soil 2 and n not = 2
That is, n = - 2
SiNx + siny + Sinz = 0, cosx + cosy + cosz = 0, find the value of COS (Y-Z)
siny+sinz=-sinx①
cosy+cosz=-cosx②
① The result is: Sin & # 178; y + Sin & # 178; Z + 2sinz + cos & # 178; y + cos & # 178; Z + 2cosycosz = Sin & # 178; X + cos & # 178; X
1+1+2sinysinz+2cosycosz=1
2cos(y-z)=-1
cos(y-z)=-½
The key is to eliminate X
sinx=-siny-sinz
cosx=-cosy-cosz
cos²x+sin²x=(cosy+cosz)²+(siny+sinz)²
=cos²y+cos²z+2cosycosz+sin²y+sin²z+2sinysinz
=2+2(cosycosz+sinysinz)
=2+2cos(y-z)=1
cos(y-z)=-1/2
(K-3) times the power of the absolute value of K of Y + 5 = K-4 is the power of one variable with respect to y
Sorting: (K-3) y ^| K | + 9-k = 0
Because it's a linear equation of one variable
therefore
k-3≠0
|k|=1
The solution is: k = ± 1
That's ± 1?
Given that x, y, Z are acute angles, and SiNx + Sinz = siny, cosx cosz = cosy, find the value of X-Y
Because Sinz = siny SiNx;
cosz＝cosx-cosy；
So square the two and add them
It can be concluded that cosx * cosy + SiNx * siny = 1 / 2
cosx*cosy＋sinx*siny＝cos（x－y）＝1／2
So X-Y = plus or minus 60 degrees
The answer is plus or minus 60 degrees
sinz＝siny－sinx；
cosz＝cosx-cosy；
Square both sides of the two formulas at the same time
And then add it up
Add the square of sincosy = 1
We can calculate the final formula: cosx * cosy + SiNx * siny = 1 / 2
cosx＊cosy＋sinx＊siny＝cos（x－y）＝1／2
To begin with
sinz＝siny－sinx；
cosz＝cosx-cosy；
Square both sides of the two formulas at the same time
And then add it up
According to Sinz's Square plus cosz's Square = 1; SiNx's Square plus cosx's Square = 1; siny's Square plus cosy's Square = 1
We can calculate the final formula: cosx * cosy + SiNx * siny = 1 / 2
cosx＊cosy＋sinx＊siny＝cos（x－y）＝1／2
So X-Y = plus or minus 60 degrees
If the function y = (M + 2) x ^ M2 2m 9 is an inverse proportional function, then the value of M is ()
If the function y = (M + 2) x ^ M2 2m 9 is an inverse proportional function, then the value of M is ()
A. M = 4 or M = - 2 B.M = 4 C.M = - 2 D.M = - 1
Is it M & sup2; - 2m-9?
The inverse scale function, then the degree of X is - 1
So M & sup2; - 2m-9 = - 1
m²-2m-8=0
(m-4)(m+2)=0
The coefficient of inverse proportion function is not equal to 0
So m + 2 ≠ 0
So M-4 = 0
M=4
Choose B
One
Given that ① 1 + cosx siny + sinxsiny = 0, ② 1-cosx-cosy + sinxcosy = 0, find the value of SiNx
From the known two formulas, we can get: 1 + cosx = siny (1-sinx) - (1) 1-cosx = cosy (1-sinx) - (2) from the sum of squares of the above two formulas: (1) square + (2) to get 2 + 2 (cosx) ^ 2 = (1-sinx) ^ 2, let z = SiNx, then (cosx) ^ 2 = 1 - (SiNx) ^ 2 = 1-z ^ 2, then 2 + 2 (1-z ^ 2) = (1-z) ^ 2, z = (1 ± √ 10) / 3 from (1) + (2) (siny + cosy) * (1-sinx) = 2, since 1-sinx ≥ 0, so siny + cosy > 0 Since siny + cosy = √ 2 (sin (y + π / 4)) ≤ √ 2, then 1-sinx ≥ √ 2 is SiNx
When m is the value, y = (m * 2 + 2m) x * (m * 2 + m-1) is the inverse proportional function
*It means in the upper right corner,
The form of inverse proportion function: y = x ^ (- 1), so there is m ^ 2 + M-1 = - 1 and m ^ 2 + 2m ≠ 0, the solution is m = - 1, so when m = - 1, f (x) is an inverse proportion function
I am also doing this question. The answer is correct, but the process is not guaranteed