The integral of the square of cosx / (sin2x), the integral of e ^ x multiplied by 1 + SiNx / 1 + cosx

The integral of the square of cosx / (sin2x), the integral of e ^ x multiplied by 1 + SiNx / 1 + cosx

Let y = SiNx, then
cosxdx/sin^2(2x)=dsinx/4sin^2xcos^2x=dy/4y^2(1-y^2)
Then take it apart
1/y^2(1-y^2)=1/y^2+(1/(1+y)+(1/1-y))/2
2. Using half angle formula
e^x(1+sinx)dx/(1+cosx)=[e^x*sec^2(x/2)/2 + e^x*tan(x/2)]dx=d(e^xtan(x/2))
What fraction of a meter is 36 cm?
1 decimeter = 10 cm
So 36 cm = 36 / 10 decimeter
Further fraction = 18 / 5 decimeter~
2cos(α＋β)＋cos2α＋cos2β＝2cos(α＋β)＋2cos(α＋β)cos(α－β
How to change this step, please be more detailed~
cos2a+cos2b=cos[(a+b)+(a-b)]+cos[(a+b)-(a-b)]
=cos(a+b)cos(a-b)-sin(a+b)sin(a-b)+cos(a+b)cos(a-b)+sin(a+b)sin(a-b)
=2cos(a+b)cos(a-b)
Integral of 1 / (1 + SiNx + cosx)
Let t = Tan (x / 2), then SiNx = (2t) / (1 + T ^ 2), cosx = (1-T ^ 2) / (1 + T ^ 2), DX = (2DT) / (1 + T ^ 2), then 1 + SiNx + cosx = 1 + [(2t) / (1 + T ^ 2)] + [(1-T ^ 2) / (1 + T ^ 2)] = (2 + 2t) / (1 + T ^ 2), that is, 1 / (1 + SiNx + cosx) = (1 + T ^ 2) / (2 + 2T so ∫ 1 / (1 + SiNx + cosx) DX = ∫ [(1 + T ^
Nine centimeters is equal to a few parts of a meter
Nine centimeters is nine tenths of a meter
=Ten to nine decimeters
9 / 100 meters
Calculation (COS Π / 7) (Cos2 Π / 7) (cos3 Π / 7)
cos∏/7·cos2∏/7·cos3∏/7
=-cos∏/7·cos2∏/7·cos4∏/7
=-2sin∏/7cos∏/7·cos2∏/7·cos4∏/7/2sin∏/7
=-sin2∏/7·cos2∏/7·cos4∏/7/2sin∏/7
=-sin2∏/7·cos4∏/7/4sin∏/7
=-sin8∏/7/8sin∏/7
=-sin(∏+∏/7)/8sin∏/7
=1/8
Let f (SiNx + cosx) = SiNx × cosx, then f (COS π / 6) =?
2sinx × cosx = (SiNx + cosx) * (SiNx + cosx) - 1, so
f（sinx+cosx）=（sinx+cosx)*（sinx+cosx）/2-1/2
f(X)=x*x/2-1/2
f（cosπ/6）=-1/8
SiNx + cosx = √ 2 * [(√ 2) / 2 * SiNx + (√ 2) / 2 * cosx] (Note: (√ 2) / 2 = 1 / (√ 2))
=√ 2 * (COS π / 4 * SiNx + sin π / 4 * cosx) (Note: sin π / 4 = cos π / 4 = (√ 2) / 2)
=√ 2 * (x + π / 4) (Note: formula of sum of two angles of trigonometric function: Sina * CoSb + SINB * cosa = sin (a + b))
And sinxcosx = 2Sin... Expansion
SiNx + cosx = √ 2 * [(√ 2) / 2 * SiNx + (√ 2) / 2 * cosx] (Note: (√ 2) / 2 = 1 / (√ 2))
=√ 2 * (COS π / 4 * SiNx + sin π / 4 * cosx) (Note: sin π / 4 = cos π / 4 = (√ 2) / 2)
=√ 2 * (x + π / 4) (Note: formula of sum of two angles of trigonometric function: Sina * CoSb + SINB * cosa = sin (a + b))
And sinxcosx = 2sin2x (double angle formula: sin2x = 2sinxcosx)
And [√ 2 * sin (x + π / 4)] ^ 2 = 2Sin (x + π / 4) ^ 2
=-cos(2x+π/2)+1
(Note: if (x + π / 4) is regarded as an angle, then 2Sin (x + π / 4) ^ 2 = 1 - {[cos (x + π / 4)] ^ 2 - [sin (x + π / 4)] ^ 2} =..., from (cosx) ^ 2 + (SiNx) ^ 2 = 1 and (cosx) ^ 2 - (SiNx) ^ 2 = cos2x -- double angle formula.)
=Sin2x + 1 (Note: there is induced formula cos (x + π / 2) = - SiNx)
sinxcosx=[(sinx+cosx)^2-1]/2
f(sinx+cosx)=[(sinx+cosx)^2-1]/2
f(x)=(x^2-1)/2
f(cosπ/6)=f(√3/2)=(3/4-1)/2=-1/8
From the problem, we can get SiNx + cosx = cos π / 6
∴（sinx+cosx)^2=3/4
∴2sinx*cosx=(sinx+cosx)^2-(sinx^2+cosx^2)=-1/4
f(cosπ/6）=-1/8
Let SiNx + cosx = cos π / 6 = radical 3 / 2
The square is 1 + 2sinx × cosx = 3 / 4
That is SiNx × cosx = 1 / 8
That is, f (COS π / 6) = f (SiNx + cosx) = SiNx × cosx = 1 / 8
How many meters does 9 decimeters equal
9/10 0.9
How many grams of money used to be equal to what it is now?
From the first emperor of Qin Dynasty to the founding of the people's Republic of China, the measurement method of one kilogram and sixteen Liang has been used in China. Sixteen Liang scale is called sixteen Venus scale, which is composed of the Big Dipper, the South dipper and the three stars of fortune, fortune and longevity
F (SiNx) = cosx, then f (COS)=
f(sinx)=cosx
f[cos(π/2-x)]=cosx
Let t = π / 2-x, x = π / 2-t
Then f (cost) = cos (π / 2-T) = Sint
∴ f(cosx)=sinx
f(cosx)=f(sin(pi/2-x))=cos(pi/2-x)=sinx