Simplify {1 + sina-2 [sin (45 ° - A / 2)] ^ 2} / [4cos (A / 2)]

Simplify {1 + sina-2 [sin (45 ° - A / 2)] ^ 2} / [4cos (A / 2)]

{1+sina-2[sin(45°-a/2)]^2}÷[4cos(a/2)]
=﹛1+sina-[1-cos(90°-a﹚]﹜／[4cos(a/2)]
=[1+sina-﹙1-sina﹚]／[4cos(a/2)]
=2sina／[4cos(a/2)]
=4sin(a/2)cos(a/2)／[4cos(a/2)]
=sin(a/2﹚

Simplification: 3 / 2cos X - (radical 3) / 2Sin x

Root 3 (root 3 / 2 * cos X-1 / 2Sin x) = root 3 (sin 60 cos x-cos 60 SiN x) = root 3 * sin (60-x)
Here we pay attention to extract the root sign 3. Why the root sign 3 is proposed, because under the root sign [(3 / 2) ^ 2 + ((root 3) / 2) ^ 2] = root 3

Simplification: 4 √ 2cos α + 3 √ 2Sin α

If sin β = 4 / 5, and β ∈ (0, π / 2), then cos β = 3 / 5. Therefore, β = arcsin (4 / 5) 4 / 5 (4 / 5) cos α + (3 / 5) sin α = 5 √ 2 [(4 / 5) cos α + (3 / 5) sin α] order: sin β = 4 / 5, and β ∈ (0, π / 2), then: cos β = 3 / 5. Therefore, β = arcsin (4 / 5) 4 √ 2cos α + 3 √ 2Sin α = √ 2 (4cos α + 3sin α) = 5 √ 2 [(4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 4 / 3 / 3 / 2) 2 (4 / 4 / 3 5) cos

Simplification, 1 / 2cos α + radical 3 / 2Sin α

Sine formula using sum of two angles
sin(A+B)=sinAcosB+cosAsinB
ν 1 / 2cos α + radical 3 / 2Sin α
=sin(π/6)*cosα+cos(π/6)sinα
Reverse the above formula
=sin(π/6+α)

Simplify cos (180 ° + x) * sin (x + 360 °) / [sin (- x-180 °) * cos (- 180 ° - x)]

cos(180°+x)*sin(x+360°)/[sin(-x-180°)*cos(-180°-x)]
=-cosx×sinx/[-sin(180°+x)][cos(180°+x)]
=-cosx×sinx/sinx(-cosx)
=1

Let f (x) = (sin ^ 2 (6 π + x) + cosx-2cos ^ 3 (3 π + x) - 3) / 2 + cos ^ 2 (x-4 π) - cos (- x) Let the (x) - cos (3) - cos (2) - cos (3) be (x) - cos (3) - cos (2) - S (2) and (2) s (2) respectively

f(x)=[sin²(6π+x)+cosx-2cos³(3π+x)-3]/2 +cos²(x-4π)-cos(-x)=(sin²x+cosx+2cos³x -3)/2 +cos²x-cosx=(1-cos²x+cosx+2cos³x -3+2cos²x-2cosx)/2=(2cos³x+cos...

Given cos (180 degrees - x) = - 3 / 5, the value of sin (360-x) is equal to Help me. It's urgent

Cos (180 degrees - x) = - cosx = - 3 / 5
cosx=3/5
sin²x+cos²x=1
So SiNx = ± 4 / 5
sin(360-x)=-sinx
So the original formula = 4 / 5 or - 4 / 5

Simplification: 1 + sin (α - 360 °) cos (α - 270 °) - 2 (COS α) ^ 2

The original formula = sin α ^ 2 + cos α ^ 2 + sin α cos (α - Π - Π - 2) - 2cos α ^ 2
=sinα^2+cosα^2+sinα[-cos(α－∏÷2)]-2cosα^2
=sinα^2+cosα^2+sinα(-sinα)-2cosα^2
=sinα^2+cosα^2-sinα^2-2cosα^2
=-cosα^2

Simplify sin (a + 30 °) + cos (a + 60 °)__________________________ The result is? 2cos (360 ° - a)

sin(a+30°）+cos(a+60°)
=cos(60°-a) +cos(60°+a)
=2cos60°cosa
=cosa

Simplify (sin (α / 2) - cos (α / 2)) * (1 + sin α + cos α) / √ (2 + 2cos α) (270 ＜ α 360)

cosa
Remember to adopt it