Simplification: cos α + sin α + a? Sin (α + π / 4)

Simplification: cos α + sin α + a? Sin (α + π / 4)

cosα+sinα+a²sin(α+π/4)
=cosα+sinα+a²（sinαcosαπ/4 +cosαsinπ/4）
=cosα+sinα+a²(sinα√2/2 +cosα√2/2)
=cosα+sinα+√2/2 a²(cosα+sinα)
=cosα+sinα(1+√2/2 a²)

Simplify sin (α - 3 / 2 π) cos (α - π) - sin (α - 2 π) cos (α - π / 2) =?

sin(α-3/2π)cos(α-π)-sin(α-2π)cos(α-π/2)
sin(α-3/2π)=sin(α+π/2)=cosα
cos(α-π)=-cosα
sin(α-2π)=sinα
cos(α-π/2)=cos(π/2-α)=sinα
Therefore, the original formula = - (COS α) ^ 2 - (sin α) ^ 2 = - 1

Simplification: sin (2 π - α) cos (π / 2 + α) + sin (3 π / 2 - α) cos (π - α)=

sin(2π-α)cos(π/2+α)+sin(3π/2-α)cos(π-α)
=（-sinα)*（-sinα)+（-cosα)*（-cosα)
=（sinα)^2+(cosα)^2=1

Simplification: (sin α) ^ 3 + (COS α) ^ 3

a³+b³=(a+b)(a^2-ab+b^2)
（sinα)^3+（cosα）^3
=(sina+cosa)*(sin^2a+cos^2-sinacosa)
=(sina+cosa)*(1-sinacosa)

Simplify sin ^ 2 (3 θ) - cos ^ 2 (3 θ)

sin²(3θ)-cos²(3θ)
= -[cos²(3θ)-sin²(3θ)]
= -cos(6θ)

Simplify cos ^ 4 angle + sin ^ 2 angle cos ^ 2 angle + sin ^ 2 angle

=(cos^2(x))^2+sin^2(x)cos^2(x)+sin^2(x)
=cos^2(x)(sin^2(x)+cos^2(x))+sin^2(x)
=cos^2(x)+sin^2(x)
=1

Simplification: (COS (π / 4 + a) - sin (π / 4 + a)) / (COS (π / 4-A) + sin (π / 4-A))

(COS (π / 4 + a) - sin (π / 4 + a)) / (COS (π / 4-A) + sin (π / 4-A)) / (COS (π / 4-A) + sin (π / 4-A)) / (COS π / 4 cos (π / 4 + A) - cos π / 4 sin (π / 4 + a)) / (COS π / 4 cos (π / 4-A) + sin π / 4 sin (π / 4-A)) = sin (π / 4 - π / 4 - a) / cos (π / 4 - π / 4)

Simplify cos (π / 3 + a) + sin (π / 6 + a)

The original formula = (1 / 2) cosa - (√ 3 / 2) Sina + (1 / 2) cosa + (√ 3 / 2) Sina
=cosa

How to simplify sin (a + b) cos (a-b) If tanb and Tana are the two roots of the equation x (square) + 2x + 5 = 0, then sin (a + b) / cos (a + b) =? I just got stuck in this one Sin (a + b) / cos (a-b) =? It should be this. The question above is wrong

The original formula Tan (a + b) = (Tana + tanb) / (1-tana * tanb)
But according to the characteristics of the root of the equation, we can only know that the sum of the two is equal to Tana + tanb = - 2, and the product of two is tanatanb = 5
The original formula can be obtained by bringing it in

Simplification: sin (3 π / 2-A) cos (2 π + a)

sin(3π/2-a)=(3π/2-a-2π)=sin(-a-π/2)=-sin(a+π/2)=-cosa
cos(2π+a) =cosa
therefore
sin(3π/2-a)cos(2π+a)
=-cosacosa
=-cos²a