Given sina0, the square of 1-sin a under the root sign=

tana=sina/cosa >0
∵sina

Simplification: subtracting (1-sina) / (1-sina) from (1-sina) / (1-sina)

In order to make Sina radical 3cosa = 4m-6 meaningful to a ∈ R, we find the value of real number M

sina-√3cosa
=2*[sina*(1/2)-cosa*(√3/2)]
=2[sinacos(π/3)-cosasin(π/3)]
=2sin(a-π/3)
In order to make Sina radical 3cosa = 4m-6 meaningful for a ∈ R
That is, 2Sin (a - π / 3) = 4m-6 is significant for a ∈ R
The value range of the function y = 2Sin (a - π / 3) is [- 2,2]
∴ 4m-6∈[-2,2]
∴ -2≤4m-6≤2
∴ 4≤4m≤8
∴ 1≤m≤2
That is, the value range of real number m is [1,2]

In teaching auxiliary angle formula: in order to make Sina radical 3 cosa = (4m-6) / (4-m) meaningful, find the value range of M?

3 cosa = (4m-6) / (4-m) 1 / 2sina - √ 3 / 2cosa = (2m-3) (4-m) 4-m) sin (A-60 °) = (2m-3) / (4-m) - 1 ≤ sin (A-60 °) ≤ 1-1 ≤ (2m-3) / (4-m) ≤ 1 (1) (2m-3) / (4-m) ≤ 1 (1) (2m-3) / (4-m) + 1 ≥ 0 (M + 1) / (M-4) ≤ 0-1 ≤ m ≤ 4 (2) (2m-3) / (4-m) - 1 ≤ 1 ≤ 0 (3m-7) / (M-4) / (M-4) ≥ 1 ≤ 0 (3m-7) / (M-4) / (M-4) ≥ ≥ ≥ 4)

It is known that sina of 3 times cosa radical is 4m-6 of 4-m, which is meaningful to find the value range of real number M

Cosa Sina with 3 times root number
=2Sin (a + 150 degrees)
So - 2 ≤ (4m-6) / (4-m) ≤ 2
-2≤(4m-6)/(4-m)
-2(4-m)^2≤(4m-6)(4-m)
(4m-6+2)(4-m)≥0
(4m-6+2)(m-4)≤0
1≤m≤4
(4m-6)/(4-m)≤2
(4m-6)(4-m)≤2(4-m)^2
(4m-6-2)(4-m)≤0
(4m-8)(m-4)≥0
m≥4,m≤2
4-m in denominator, M is not equal to 4
So 1 ≤ m ≤ 2

It is known that sina = 2 radical 5 / / 5, π / 2

sina=2√5/5
sin^2a=4/5
cos^2a=1/5
Because π / 2

Given △ ABC, a = 1, B = root 2, C = root 5, Sina = - 5, root 5, find the size of (1) angle c (2) sin2 (c + a)

cosC=(a²+b²-c²)/(2ab)
=(1+2-5)/(2√2)=-√2/2
∵ C is the inner angle of the triangle
∴C=3π/4
(2)
Sina = - √ 5 / 5 is problematic and it is not necessary to give it
According to the cosine theorem
cosB=(a²+c²-b²)/(2ac)
=(1+5-2)/(2√5)
=2√5/5
sinB=√5/5
sin2(C+A)
=sin2[180º-B]
=sin(360º-2B)
=-sin2B
=-2sinBcosB
=-2*√5/5*2√5/5
=-4/5

It is known that sina = 2 * radical 5 / 5, π / 2

-2. Calculate cosa according to Sina, the square of sina + the square of cosa = 1, and because the range of a is in the distribution of half, cosa = negative root 5 divided by 5. So Tana = Sina / cosa

1: Let P (x, negative root 2) x of the final edge of angle a is not equal to 0, and cosa = (root 3) x divided by 6. Find the value of sina Tana

Let x = = = = = = = = = = =) = = = = = = =) = = = = = =) = = = = = = =) = = = = = =) = = = = = =) = = = = = =) = = = = = =) = = = = = = =) = = = = = = = =
Cosa = = (root 3) exes divided by 6
Sinatana = Tana * cosa * Tana = Tan ^ 2 * cosa = root three divided by X
Well, I don't know if the result is right or not. The method is similar. Is there a screenshot of the question? If you don't understand it correctly, you should have the same question. Please leave me a message

Given a point P (- 9t, 12t) on the final edge of angle a (t is not equal to 0), find the value of sina cosa Tana

Defined by trigonometric functions
Point on the final edge of corner (x0, Y0)
SiNx = x0 / radical (x0 ^ 2 + Y0 ^ 2)
Cosx = Y0 / radical (x0 ^ 2 + Y0 ^ 2)
tgx=x0/y0
therefore
T>0
sinx=-3/5
cosx=4/5
tgx=-3/4
T

Given sina0, the square of 1-sin a under the root sign=