How to simplify sin (a + b) cosa cos (a + b) Sina

How to simplify sin (a + b) cosa cos (a + b) Sina

Formula: sin (α ± β) = sin α. Cos β ± cos α. Sin β
sin(a+b)cosa-cos(a+b)sina=sin(a+b-a)=sinb

Simplify Sina + sin (a + 2 / 3 π) + cos (a + 5 / 6 π) RT

sinA+sin（A+2/3π）+cos（A+5/6π）
=sina+sinacos2/3pai+sin2/3paicosa+cosacos5/6pai-sinasin5/6pai
=Sina-1 / 2sina + root 3 / 2cosa - root 3 / 2cosa-1 / 2sina
=0

Find the value of sina + sin (120 ° + a) + sin (240 ° + a)

sinA+sin(120°+A)+sin(240°+A)=sinA+sin(180°-60°+A)+sin(180°+60°+A)=sinA+sin(60°-A)-sin(60°+A)=sinA+sin60°cosA-cos60°sinA-(sin60°cosA+cos60°sinA)=sinA-2cos60°sinA=sinA-sinA=0

Let a = (4cosa, Sina), B = (sin β, 4cos β), C = (COS β, cos β) Question: (1) if a is perpendicular to b-2c, find the value of Tan (a + β) (2) Find the maximum value of | B + C | (3) If tanatan β = 16, a / / b

1. If a is perpendicular to b-2c, the inner product of vector a and vector (b-2c) is 0
(4cosa, Sina) * (sin β, 4cos β)
=4cosasinβ+4sinacosβ=0,
So sin (a + β), = 0
tan(a+β)=0
2.b+c=(sinβ+cosβ,4cosβ+cosβ)
So | B + C | = radical [(sin β + cos β) ^ 2 + (5cos β) ^ 2]
=Radical [sin2 β + (Cos2 β) / 2 + 27 / 2]
=Radical [[(Radix 5) sin (2 β + T)] / 2 + 27 / 2] (where tant = 1 / 2)
Therefore, the maximum value is the root sign [[(root 5) + 27] / 2]
3. Tanatan β = 16, that is, sinasin β = 16 cosacos β
So a / / b

Reduce (2cos ^ 2 · A-1) / (1-2sin ^ 2 · a) to be equal to?

（2(cos a)^2-1）/（1-(2sin a)^2）=cos 2a/cos 2a=1

Simplification (2) 2Sin 2 α - 1 / 1-2cos 2 α

0

0

（2cos²a-1）/（1-2sin²a）
Double angle formula of cosine
The original formula = cos2a / cos2a = 1
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Simplification: (1) the square a of 2cos-1 / 1-2sin; (2) the square of root 1-sin is 100 ° Simplification: (1) the square a of 2cos-1 / 1-2sin; (2) the square of root 1-sin is 100 ° Urgent, today, we need to write the process, now we need to

1) The square of 2cos A-1 / 1-2sin
=cos2a/cos2a
=1
2) The square of root 1-sin is 100 °
=√(1-sin100°)(1+sin100°)
=√(1-2sin50°cos50°)(1+2sin50°cos50°)
=√(sin50°-cos50°)^2(sin50°+cos50°)^2
=(sin50°-cos50°)(sin50°+cos50°)
=sin^2 50°-cos^2 50°
=-cos100°
=cos80°

Radical 3 / 2Sin α - 1 / 2cos α=

Radix 3 / 2Sin α - 1 / 2cos α = cos 30 ° sin α - sin30 ° cos α = sin (α - 30 °)

If the angle satisfies 1 / 2cos α - radical 3 / 2Sin α = 1, then What is the angle equal to?

Write 1 / 2 as cos 60 ° and √ 3 / 2 as sin 60 °
The original formula is as follows:
cosacos60°-sinasin60°=1
That is, cos (a + 60 °) = 1
Then: a + 60 degree = k * 360 degree
A = - 60 ° and K * 360 ° were obtained
That is, π - 2K = - 2K