It is known that cos2 7 25, 2 is the value of tan

cos(2θ)=7/25

cos 2(2)-sin 2(2)=7 251-2sin 2( )=7 25, so sin =3 5

According to the hook three strands four Xuan five, we get cos = 4 5, but it is the second quadrant, so cos = -4 5

tan is -3 4

a-b|This is not an absolute value, this is called the "modulus" of the vector

According to the question, the equation is obtained: sqrt() is the meaning of the open square, and the parentheses are under the root number.

sqrt((cosα-cosβ)^2+(sinα-sinβ)^2)=2sqrt(5)/5

Inside Squared: Get:

sqrt(1+1-2cos( -=2sqrt(5) 5 simplification:cos( -=3 5

1.Due to 2 < <

Then: sin >0, cos <0

Because. cos2θ

1-2sin^2(θ)

Then: sin = 3 5

Then: cos

Root number [1-sin 2 ( )

Then: tan

sinθ/cosθ

Because. a=(cos,sin),b=(cos,sin) then:a-b

cos, sin)-cos, sin) (cos-cos, sin -sin) then: a-b) 2

cosα-cosβ)^2+（sinα-sinβ)^2(cos^2(α)sin^2(α)cos^2(β)sin^2(β)2[cosαcosβ+sinαsinβ]

2-2cos（α-

(a-b) 2

a-b|^2

Then: 2-2cos( -=4 5

Then: cos( -=3 5

Solution: tan = [1 2] is known from the known

1) Since tan is known, it is considered to turn the formula into a tangent form, and combined with tan = [sin cos], it can be seen that the numerator and denominator of the formula are divided at the same time.

cos.

2) Same as (1), but the sought formula has no denominator, so it is first transformed into the form of fraction, the denominator is added with 1, and 1=sin 2 + cos 2, the same as (1) below

It is known that tan = [1 2].

1）[sinα−3cosα/sinα+cosα＝tanα−3

tanα+1＝−

2）sin2α+sinαcosα+2

sin2α+sinαcosα+2（cos2α+sin2α）3sin2α+sinαcosα+2cos2αsin2α+cos2α

3tan2α+tanα+2

tan2α+1

5,9,Knowing [tan tan 1]=-1, find the values of the following formulas:

1）[sinα−3cosα/sinα+cosα]；

2）sin 2α+sin αcos α+2．

Its value is equal to -3. Because -27=(-3), then Radical Brigade -27=(-27) (1 3), can be expressed as ((-3) )1 3)=(3) (3*1 3)=(3) 1=-3.

The root number 9 is equal to 3, and the root number of minus 27 to the 3rd power is equal to -3, so the original formula is equal to 9