Given sin α + sin β = 1 and cos α + cos β = 0, what is the value of Cos2 α + Cos2 β? (calculation process required) Thank you first~

Given sin α + sin β = 1 and cos α + cos β = 0, what is the value of Cos2 α + Cos2 β? (calculation process required) Thank you first~

The sum and difference should not be changed
cosα+cosβ=0
Then cos α = - cos β
α=(2k+1)π-β k∈Z
Sin α = sin [(2k + 1) π - β] = sin β
Sin α + sin β = 1
sinα=sinβ=1/2
cos2α=1-2(sinα)^2=1-2(sinβ)^2=cos2β=1/2
cos2α+cos2β=1

What is sin (0.5 degrees) equal to What is sine 0.5 degrees equal to,

zero point zero zero eight seven two six five three five four nine eight

Why is sin (π / 4-x) equal to cos (x + π / 4)

sin(π/4-x)=sin(π/4)cosx-cos(π/4)sinx=（√2/2）cosx-（√2/2）sinx;
cos(x+π/4)=cosxcos(π/4)-sinxsin(π/4)=（√2/2）cosx-（√2/2）sinx；

Given sin α + cos α / 2Sin α - cos α = 2, calculate the value of Tan α

sinα+cosα/2sinα-cosα=2
sinα+cosα=4sinα-2cosα
So sin α = cos α
So tan α = sin α / cos α = 1

Using trigonometric function line to find the value of angle X satisfying SiNx = √ 2 / 2 and the range of angle X satisfying SiNx ＞ 2 / 2

Draw a unit circle with the center of the circle at the origin, find the position of 0.7 (√ 2 / 2) on the y-axis, draw a straight line parallel to the x-axis, intersect the circle at two points P and Q, ∠ pox = 45 ° and ∠ qox = 135 ° and SiNx ＞ 2 / 2 fall to the middle of 45 ° and 135 ° respectively, so the angle between 0 and 360 ° is 45 °

Given that a is greater than 0 and B is greater than 0, it is proved that 2Ab / A + B is less than or equal to the root sign AB is less than or equal to a + B / 2 less than or equal to a square plus b square / 2 under the root sign

One
Suppose that 2Ab / (a + b) > AB under the radical sign AB, then both sides of the square and reduce AB have 4AB / (a * a + b * B + 2Ab) > 1, then there is a * a + b * b-2ab (a + b) / 2. As above, we can get that the complete square of A-B is less than 0;
Three
Under the root sign, the complete square of a square plus b square / 2 is equal to (a square plus b square) / 2. By subtracting the complete square of (a + b) / 2, the complete square of (a * a + b * b-2ab) / 4 = (a-b) / 2 is obviously greater than or equal to 0
Take a closer look

It is proved that: 1 / [root 2 + root 3] > root 5-2

√5-2
=√5-√4
=(√5-√4)(√5+√4)/(√5+√4)
=1/(√5+√4)
∵√5>√3
√4>√2
∴√5+√4>√3+√2
/ / 1 / (√ 5 + √ 4) root 5-2

Total differential of x square + y square under z = Y / radical

∵z=y/√(x²+y²)
∴dz=d(y/√(x²+y²))
=[√(x²+y²)dy-yd(√(x²+y²))]/[√(x²+y²)]²
=[√(x²+y²)dy-y(xdx+ydy)/√(x²+y²)]/[√(x²+y²)]²
=[x(xdy-ydx)]/[√(x²+y²)]³.

0

1 / (x root x)
Don't you remember the formula and use the formula

Root 75 plus 3 / 3 minus 48

The root sign 75 is equal to 5 root sign 3, 3 root sign 1 / 3 equals root sign 3, root sign 48 equals 4 root sign 3, the original title is equal to 5 root sign 3 plus root sign minus 4 root sign 3, and finally equals 2 root sign 3