Find the value of (1 / 1 - sin a) + (1 / 1 + sin a) when Tan a = 3 Given Tan a = 3, find the value of 1 / (1 - sin a) + 1 / (1 + sin a)

Find the value of (1 / 1 - sin a) + (1 / 1 + sin a) when Tan a = 3 Given Tan a = 3, find the value of 1 / (1 - sin a) + 1 / (1 + sin a)

1/(1-sina)+1/(1+sina)=(1+sina+1-sina)/(1-sina)(1+sina)
=2/cos^2a tana=3 cos^2a=1/10
=2*10
=20

It is known that Tan α and Tan β are two of the equations 6x2-5x + 1 = 0, and 0 < α < π 2, π < β < 3 π 2. The values of Tan (α + β) and α + β are obtained

∵ Tan & nbsp; α, Tan & nbsp; β are two of the equations 6x2-5x + 1 = 0, ∵ Tan α + Tan β = 56, Tan α Tan β = 16, Tan (α + β) = Tan α + Tan β 1 − Tan α Tan β = 561 − 16 = 1. ∵ 0 < α < π 2, π < β < 3 π 2, ∵ π < α + β < 2 π, ∵ α + β = 5 π 4

Given Tan (x / 2) = 1 / 2, the value of sin (x + π / 6) is obtained=

If Tan (x / 2) = 1 / 2sinx / (1 + cosx) = 1 / 21 + cosx = 2sinx2sinx cosx = 1 and sin ^ 2x + cos ^ 2x = 1, then the two equations are simultaneous. The solution is SiNx = 4 / 5, cosx = 3 / 5 or SiNx = 0, cosx = - 1 and SiNx / (1 + cosx) = 1 / 2, SiNx = 4 / 5, cosx = 3 / 5sin (x + π / 6) = SiNx * cos (π / 6) + C

What are trigonometric functions for
For cosine theorem, sine theorem is of little use, and its concrete function is unknown

It can be used to calculate the size of edges and corners in high school, and it is also very useful in calculating limits in College (such as lobita's law)

Trigonometric function problem
Sin ^ 2 (X-30) + cos ^ 2 (X-60) + sinxcosx the numbers in this function are angles. How to simplify this function

=〔1- cos2(x-30) 〕/2+〔1- cos2(x-60) 〕/2+sin2x/2=1-〔-cos2x/2-sin2x(√3)/2-cos2x/2+sin2x(√3)/2〕+sin2x/2=1-( sin2x- cos2x)/2=1- cos45 sin(2x-45)=1-〔(√2)/2〕sin(2x-45)

On trigonometric function
If the function f (x) = 2sinx has f (x1) ≤ f (x) ≤ f (x2) for X ∈ R, what is the minimum value of x1-x2?

f(x1)≤f(x)≤f(x2)
That is, f (x1) is the minimum and f (x2) is the maximum
The difference between the maximum and minimum of sine function is at least half a period
So let Lee t = 2 π
So | x1-x2 | min = t / 2 = π

The problem of trigonometric function
Asina + bcosa = a ^ 2 + B ^ 2 under the root sign, and then multiply by sin (a + arctan (B / a))
But after - Asina bcosa reduction, it is not equal to a ^ 2 + B ^ 2 under the root sign, and then multiplied by sin (a + arctan (B / a)). But Asina + bcosa and - Asina bcosa are not equal. Why? What are the restrictions of a and B?

"- Asina bcosa after simplification is also equal to a ^ 2 + B ^ 2 under the root sign, and then multiplied by sin (a + arctan (B / a))" is wrong
It is equal to a ^ 2 + B ^ 2 under - root, and then multiplied by sin (a + arctan (B / a)), with a negative sign in front

What is the relationship between trigonometric functions of the same angle?

The common method is SiNx ^ 2 + cosx ^ 2 = 1
tanx^2-1=1/cosx^2
tanx*cotx=1
Basic relations of trigonometric functions with the same angle
Reciprocal relation: quotient relation: square relation:
tanα ·cotα＝1
sinα ·cscα＝1
cosα ·secα＝1 sinα/cosα＝tanα＝secα/cscα
cosα/sinα＝cotα＝cscα/secα sin2α＋cos2α＝1
1＋tan2α＝sec2α
1＋cot2α＝csc2α
Induction formula
sin（－α）＝－sinα
cos（－α）＝cosα tan（－α）＝－tanα
cot（－α）＝－cotα
sin（π/2－α）＝cosα
cos（π/2－α）＝sinα
tan（π/2－α）＝cotα
cot（π/2－α）＝tanα
sin（π/2＋α）＝cosα
cos（π/2＋α）＝－sinα
tan（π/2＋α）＝－cotα
cot（π/2＋α）＝－tanα
sin（π－α）＝sinα
cos（π－α）＝－cosα
tan（π－α）＝－tanα
cot（π－α）＝－cotα
sin（π＋α）＝－sinα
cos（π＋α）＝－cosα
tan（π＋α）＝tanα
cot（π＋α）＝cotα
sin（3π/2－α）＝－cosα
cos（3π/2－α）＝－sinα
tan（3π/2－α）＝cotα
cot（3π/2－α）＝tanα
sin（3π/2＋α）＝－cosα
cos（3π/2＋α）＝sinα
tan（3π/2＋α）＝－cotα
cot（3π/2＋α）＝－tanα
sin（2π－α）＝－sinα
cos（2π－α）＝cosα
tan（2π－α）＝－tanα
cot（2π－α）＝－cotα
sin（2kπ＋α）＝sinα
cos（2kπ＋α）＝cosα
tan（2kπ＋α）＝tanα
cot（2kπ＋α）＝cotα
(where k ∈ z)
Trigonometric function formula and universal formula of sum and difference of two angles
sin（α＋β）＝sinαcosβ＋cosαsinβ
sin（α－β）＝sinαcosβ－cosαsinβ
cos（α＋β）＝cosαcosβ－sinαsinβ
cos（α－β）＝cosαcosβ＋sinαsinβ
tanα＋tanβ
tan（α＋β）＝——————
1－tanα ·tanβ
tanα－tanβ
tan（α－β）＝——————
1＋tanα ·tanβ
2tan(α/2)
sinα＝——————
1＋tan2(α/2)
1－tan2(α/2)
cosα＝——————
1＋tan2(α/2)
2tan(α/2)
tanα＝——————
1－tan2(α/2)
Sine, cosine and tangent formulas of half angle
The formula of sine, cosine and tangent of double angle the formula of sine, cosine and tangent of triple angle
sin2α＝2sinαcosα
cos2α＝cos2α－sin2α＝2cos2α－1＝1－2sin2α
2tanα
tan2α＝—————
1－tan2α
sin3α＝3sinα－4sin3α
cos3α＝4cos3α－3cosα
3tanα－tan3α
tan3α＝——————
1－3tan2α
Sum difference product formula of trigonometric function
α＋β α－β
sinα＋sinβ＝2sin—－－·cos—－—
2 2
α＋β α－β
sinα－sinβ＝2cos—－－·sin—－—
2 2
α＋β α－β
cosα＋cosβ＝2cos—－－·cos—－—
2 2
α＋β α－β
cosα－cosβ＝－2sin—－－·sin—－—
2 2 1
sinα ·cosβ＝-[sin（α＋β）＋sin（α－β）]
two
one
cosα ·sinβ＝-[sin（α＋β）－sin（α－β）]
two
one
cosα ·cosβ＝-[cos（α＋β）＋cos（α－β）]
two
one
sinα ·sinβ＝－ -[cos（α＋β）－cos（α－β）]
two
The form of trigonometric function for transforming asin α ± bcos α into an angle (the formula of trigonometric function of auxiliary angle)

What is the meaning of the basic relation between trigonometric functions of the same angle?
Well, I'm a freshman. My mother asked me to learn functions by myself in advance, so maybe I can't understand some things. Please forgive me
[formula from Baidu Encyclopedia]
The square relation is as follows
sin^2(a)+cos^2(a)=1
^What does it mean? (a) what does it mean?
Business relationship:
tana=sina/cosa cota=cosa/sina
I didn't understand the whole formula I don't know what it is if I add an a after the function symbol
Well, that's it. Thank you!

What are the trigonometric functions of the same angle

sin^2+cos^2=1
tan*cot=1
tan^2+1=sec^2
1+cot^2=csc^2
tan*cos=sin
sin*cot=cos
cos*csc=cot
sin*sec=tan
tan*csc=sec
sec*cot=csc