Tan (@ 8-pai) = 2, find Tan (@ - Pai / 8)

Tan (@ 8-pai) = 2, find Tan (@ - Pai / 8)

If it is known that Tan (α + 8 / π) = 2, the solution is as follows:
It is known that Tan (α + 8 parts π) = 2, then:
Tan (π of α - 8)
=Tan (α + 8 parts π - 4 parts π)
=[Tan (α + 8 of π) - Tan (of 4)] / [1 + Tan (α + 8 of π) * Tan (4 of π)]
=(2-1)÷(1+2)
=1÷3
=1 / 3

How to solve 2 / Tan (x) = 3 / Tan (45-x)?

2/tan(x)=3/tan(45-x)=3*{（1+tanx）/（1-tanx）}
That is, 2 / Tan (x) = 3 × {(1 + TaNx) / (1-tanx)}
After finishing, 3tan? X + 5tanx-2 = 0
The solution is Tan = 1 / 3 or tan = - 2

What is the angle of Tan = 1 / 2 Thank you!

Within 90 degrees
Tan 26.565 degree = 1 / 2

tan(π/2+1)=?tan(1-π/2)=?

tan(π/2+1)=-cot1
tan(1-π/2)=-tan(π/2-1)=-cot1

Given sin (π - α) = ㏒8 (1 / 4) and α∈ (- π / 2,0), find Tan (3 π / 2 + α)

By sin (π - α) = sin α, and ㏒ 8 (1 / 4) = - 2 / 3, sin α = - 2 / 3
Tan α = - 2 / (Radix 5)
Then Tan (3 π / 2 + α) = - cot α = (radical 5) / 2

It is known that Tan (π / 4 + a) = 1 / 2 Find cos2a / sin2a + cos? A

Tan π / 4 = 1, so (1 + Tana) / (1-tana) = 1 / 22 + 2tana = 1-tanatana = - 1 / 3sina / cosa = Tana = - 1 / 3cosa = - 3sina, then cos? A = 9sin? A because sin? 2A + cos? A = 1, so sin? 2A = 1 / 10, cos? 2A = cos? A-SiN? A

Let Tan (α + 8 π / 7) = a to verify: [sin (15 π / 7 + α) + 3cos (α - 13 π / 7)] / [sin (20 π / 7 - α) - cos (α + 22 π / 7)] = a + 3 / A + 1

Let x = α + 8 π / 7, then TaNx = a
∴15π/7+α=π+（α+8π/7）=π+x
α-13π/7=(α+8π/7)-3π=x-3π
20π/7-α=4π-(α+8π/7)=4π-x
α+22π/7=(α+8π/7)+2π=x+2π
Thus, on the left side of the original equation:
Left = [sin (π + x) + 3cos (x-3 π)] / [sin (4 π - x) - cos (x + 2 π)]
=(-sinx-3cosx)/(-sinx-cosx)
=(sinx+3cosx)/(sinx+cosx)
=[(sinx+3cosx)/cosx]/[(sinx+cosx)/cosx]
=(tanx+3)/(tanx+1)
=(a+3)/(a+1)

Why is a 3 π / 8 when Tan 2A = - 1 Let a be an acute angle, and Tan a + B = 3, tana-b = 2, then the angle a is equal to?

tan2a=tan(a+b+a-b)
=[tan(a+b)+tan(a-b)]/[1-tan(a+b)tan(a-b)]
=(3+2)/(1-6)
=-1
∴2a=kπ-π/4
a=kπ/2-π/8
∵ A is an acute angle,
When k = 1, a = 3 π / 8

Tan = 8 / 15

Arctan 8 / 15 = 28.07245 degrees

tan(π/8)=?

tan(π/4)==2tan(π/8)/[1-tan(π/8)^2]=1
2tan(π/8)=1-tan(π/8)^2
[tan(π/8)+1]^2=2
tan(π/8)=√2 - 1