If cot (α - Pie) = - 3 / 4, sin α (1-cot α) + cos α (1-tan α) +cscαsecα=

If cot (α - Pie) = - 3 / 4, sin α (1-cot α) + cos α (1-tan α) +cscαsecα=

sinx=4/5

It is proved that sin (α + β) / cos (α - β) = Tan α + Tan β / 1 + Tan α Tan β

prove:
It can be proved from left to right
Left = sin (α + β) / cos (α - β)
=(sinαcosβ+cosαsinβ)/(cosαcosβ+sinαsinβ)
Divide the denominator by cos α cos β at the same time
=(tanα+tanβ)/(1+tanαtanβ)
=Right
∴ sin(α+β)/cos(α-β)=tanα+tanβ/1+tanαtanβ

Given Tan (π - a) = m ^ 2, the absolute value of COS (π - a) = - cosa, find the value of COS (π + a)______

According to the known conditions, a belongs to the second quadrant, cos (π + a) = cos (a - π) = cos (π - a) = - cosa > 0
tan(π-a)=m^2=-tana
The rest draw the answer directly

Given that a and B are acute angles, cosa = 4 / 5, Tan (a-b) = - 1, find the value of COS ((a + b) / 2) * cos ((a-b) / 2)

Cosa = 4 / 5 Sina = 3 / 5 Tana = 3 / 4 Tan (a-b) = (Tana tanb) / (1 + tanatanb) = (3 / 4-tanb) / (1 + 3tanb / 4) = - 1 / 3 tanb = 13 / 9 (tanb) ^ 2 = 169 / 81 = (1 - (CoSb) ^ 2) / (CoSb) ^ 2 (CoSb) ^ 2 = 1 / (1 + 169 / 81) = 81 / 250 because B is an acute angle, CoSb = 9 / 5 √ 10 = 9 √ 10 / 50

If cos α = 3 / 5 and α is the fourth quadrant angle, then the value of Tan α is?

cos²α=1-sin²α=1-（16/25）=9/25
α is the third quadrant angle
cosα

Given that cos = 4 / 5 and α is the fourth quadrant angle, what is the value of Tan α?

∵ α is the fourth quadrant angle
∴sinα

If a is the fourth quadrant angle, Tan α = - 5 / 12, find cos α

tanα=-5/12
cosα = 12/13

If cos α = 2 / 3 and α is the fourth quadrant angle, then Tan α is equal to

Because a is the fourth quadrant angle, from the meaning of the title: Sina < 0
From cos ^ 2 + sin ^ 2 = 1, Sina = - (radical 5) / 3 is obtained
Because Tana = Sina / cosa = - (radical 5) / 2

It is proved that the angle θ is the third or fourth quadrant angle if and only if cos θ × Tan θ < 0

It is proved that the angle θ is the third or fourth quadrant angle
Then sin θ < 0
And cos θ × Tan θ = sin θ
So the angle θ is the third or fourth quadrant angle if and only if cos θ × Tan θ < 0

Given that 2Sin β = sin (2 α + β), find the value of Tan (α + β): Tan β Notice that it's Tan beta, not alpha

2sinβ=2sin(α+β-α)=2sin(α+β)cosα-2cos(α+β)sinα2sinβ/(cos(α+β)sinα)=2sin(α+β)cosα/(cos(α+β)sinα)-2=2tan(α+β)/tanα-2sin(2α+β)＝sin(α+β)cosα＋cos(α+β)sinαsin(2α+β)/(cos(α...