If 4cos α - (2 + 2 √ 3) cos α + √ 3 = 0, calculate the acute angle α

If 4cos α - (2 + 2 √ 3) cos α + √ 3 = 0, calculate the acute angle α

The factorization is (2cosa-1) (2cosa-3) = 0
It is concluded that cosa = 1 / 2 or 1 / and a = 60 degrees or 30 degrees

To prove, (COS α + cos β) &# 178; + (sin α + sin β) &# 178; = 4cos & # 178; [(α - β) / 2]

Certification:
Left = 2 + 2cos α cos β + 2Sin α sin β
=2+2cos（α-β）
∵cos（α-β）=2cos²[（α-β）/2]-1
Left = 2 + 4cos & # 178; [(α - β) / 2] - 2=
4cos & # 178; [(α - β) / 2] = right
Left = right

4cos²α－﹙2+2sqrt3﹚cosα＋sqrt3=0

4cos²α－﹙2+2sqrt3﹚cosα＋sqrt3=0
4cos²α－﹙2+2√3﹚cosα＋√3=0
（2cosα-√3）（2cosα-1）=0
2cosα-√3=0
cosα=√3/2
α = 2K π + π / 6 (k is an integer)
Or:
2cosα-1=0
cosα=1/2
α = 2K π + π / 3 (k is an integer)

If a is known to be an acute angle and Sina = x / (10) - 1, then the absolute value (X-10) + absolute value (x-20) is reduced=

A is the acute angle
0

Reduce 4cos ^ 2 (B / 2) (B is acute angle)

Double angle formula
cosB
=cos[2×(B/2)]
=cos²(B/2)-sin²(B/2)
=cos²(B/2)-[1-cos²(B/2)]
=2cos²(B/2)-1
2cos²(B/2)=cosB+1
simple form
=2×2cos²(B/2)
=2×(cosB+1)
=2cosB+2

If α is an acute angle, the result of simplifying √ (1-sin α - cos α) 2 is
If α is an acute angle, the result of simplifying √ (1-sin α - cos α) 2 is ()
A.1-sinα-cosα
B.sinα-cosα-1
C.sinα+cosα-1
D. Not sure

The correct answer is C
The results show that 1-sin α - cos α = 1 - √ 2Sin (α + π / 4),
∵0

Finding Tan α with 6sin ^ (2) α - 13sin α cos α + 6 = 0
1 find Tana
2 for Sina * cosa

1
tana=t
6sin^(2)α-13sinαcosα+6=0
6sin^(2)α-13sinαcosα+6(sin^2a+cos^2a)=0
12sin ^ (2) α - 13sin α cos α + 6cos ^ 2A = 0 (except cos ^ 2a)
12t^2-13t+6=0
Discrimination 13 ^ 2-12 * 3 * 4 = - 119

Let Tan (a) = 2. Find 5sin (a) times cos (a)

Sina = 2cosa, because Sina square + cosa square = 1, so cosa square = 0.2, 5sin (a) times cos (a) = 2

To know Tan a = - 4 / 3, find the value of (1) Tan (a + π / 4), (2) 6sin a + cos A / 3sin a-2cos a

(1) Tan (a + π / 4) = (Tana + tanpai / 4) / (1-tanatanpai / 4) = (- 4 / 3 + 1) / (1 + 4 / 3 * 1) = - 1 / 7, (2) 6sin a + cos A / 3sin a-2cos a, (the numerator is divided by COSA) = (6tana + 1) / (3tana-2) = (6 * (- 4 / 3) + 1) / (3 (- 4 / 3) + 2) = (- 7) / (- 2) = 7 / 2

Simplification: Cos2 (π 4-A) + Cos2 (π 4 + a)=______ ．

∵ (π 4-A) + (π 4 + a) = π 2, ∵ Cos2 (π 4-A) + Cos2 (π 4 + a) = Cos2 (π 4-A) + sin2 (π 4-A) = 1