a cos, sin , b cos, sin , a b 4 5, 8, find the value of tan 10

a=(cosα,sinα),b=(cosβ,sinβ).

There are two cases for the primary value:

There are two summary cases corresponding to each.

tan(α+

tan(π/8+π/8-arctan3/4)(1-tanβ)/(1+tanβ)

Or. tan(α+

tan(π/8+π/8+arctan3/4)(1+tanβ)/(1-tanβ)

Solution: a·b=4 5.

cos( 4 5 get sin( =3 5 or -3 5cos( +=cos(( 2 ) cos( ( 4) = cos( cos( 4)-sin( sin( 4) = 7*(2 or (2

Therefore sin( +2 or 7*(2

Therefore tan( +1 7 or 7

Summary. Extended Information: Addition and Subtraction Elimination of Common Methods for Solving Binary Linear Equations:

The general steps of addition and subtraction elimination are as follows: 1. In the binary system of one-dimensional equations, if there are coefficients of the same unknown number are the same (or opposite to each other), they can be directly subtracted (or added) to eliminate an unknown; 2. In the system of binary linear equations, if there is no such thing as in, an appropriate number can be selected to multiply both sides of the equation, so that the coefficients of one of the unknown numbers are the same (or opposite to each other), and then the two sides of the equation are subtracted (or added) respectively, and an unknown number is eliminated to obtain a unary equation; 3. Solve this unary equation; 4. Substituting the solution of the unary linear equation into the equation with the relatively simple coefficients of the original equation to find the value of another unknown; 5. The values of the two unknowns obtained are connected in curly brackets, which is the solution of the binary system of equations.

a+b=58+a+b/4=37+a=__

Hello Qiqin, hello, a+b=58, a+b 4=37, limb a=30, b=28The calculation process is as follows: a+b=58(1) a+(b4)=37 (2) (1)-(2), and we get:

3/4×b=58-37 b=21×4/3 b=7×4 b=28 a=58-28 a=30

Extended Information: Addition and Subtraction Elimination: The general steps of addition and subtraction are as follows:

1. In the binary system of linear equations, if there are the same coefficients of the same unknown (or opposite to each other), it can be directly subtracted (or added) to eliminate an unknown; 2. In the system of binary linear equations, if there is no such thing as in, you can choose an appropriate number to multiply both sides of the equation so that the coefficients of one of the unknown numbers are the same (or opposite to each other), and then subtract (or add) the two sides of the Bijuenxian equation respectively, eliminate an unknown number, and obtain a unary equation; 3. Solve this unary equation; 4. Substitute the solution of the unary equation into the equation with the relatively simple coefficients of the original equation, and find the value of an unknown number in another friend; 5. The values of the two unknowns obtained by the regret beat are connected in curly braces, which is the solution of the binary system of equations.

tana=tan(a-b+b)

tan(a-b)+tanb] [1-tan(a-b)*tanb](1 2-1 7) Peizi Bend (1+1 2*1 7)1 with 3

So. tan(2a-b)=tan(a+a-b)[tana+tan(a-b)]/1-tana*tan(a-b)]

tan[π/4+α]

tanπ/4+tanα)/1-tanπ/4tanα)=1+sinα/cosα)/1-sinα/cosα)

cosα+sinα)/cosα-sinα)=2cos^2(α)2cosαsinα]/2cos^2(α)2cosαsinα]

1+cos2α+sin2α]/1+cos2α-sin2α]=1+a+b)/(1-a+b)

tan[π/4+α]

tanπ/4+tanα)/1-tanπ/4tanα)=1+sinα/cosα)/1-sinα/cosα)

cosα+sinα)/cosα-sinα)=2cosαsinα+2sin^2(α)2cosαsinα-sin^2(α)

sin2α+1-cos2α]/sin2α-1+cos2α]=a+1-b)/(a-1+b)

tan[π/4+α]

sin(π/4+α)cos(π/4+α)sinα+cosα)/cosα-sinα)

sinα+cosα)^2/[(cosα-sinα)(sinα+cosα)]1+2sinαcosα)/cos^2(α)sin^2(α)

1+sin2α)/cos2α=(1+a)/b

tan[π/4+α]

sin(π/4+α)cos(π/4+α)sinα+cosα)/cosα-sinα)

(sinα+cosα)(cosα-sinα)]cosα-sinα)^2]=[cos^2(α)sin^2(α)1-2sinαcosα)

cos2α/(1-sin2α)=b/(1-a)

These four expressions are equal and can be converted using a 2 + b 2 = 1.

For example: (1+a+b) (1-a+b).

(b+1+a)(b-1-a)]/a+b+1)(-a+b-1)]=b^2-(1+2a+a^2)]/a^2+b^2-2ab)-1]

-2a-2a^2]/[2ab]=(1+a)/b

has been annihilated to let the Zhishi bureau a = 4, b -a = 1 2c , then according to the sinusoidal theorem there is:

sin b - sin a = 1 2sin c, i.e.

2sin b - 1 = sin c, the order of decline is:

1 - cos2b - 1 = 1 - cos2c) 2, i.e. .

cos2c - 2cos2b = 1, and since a = 4, b + c = 3 4, then:

cos2c - 2cos2(3 4 - c) = 1, cos2c - 2cos(3 2 - 2c) = 1.

2sin2c = 1 - cos2c, ie.

4sinccosc = 2sin c, ie.

tanc = 2

b -a =1 2c has a =b -1 2c and then according to the cosine theorem:

b + c -2bccosa = a = b -1 2c , then.

3 2c = 2bc, then c = 2 2 3b, and the substitution sub s=1 2bcsina=7 has.

b = early 21

A b is to find the intersection of a and b, and naturally get a Bi Liang b =

A b is the union of all subsets of a and b that naturally gives the number fiber a b=