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

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

sin²(a-π/2)=cos²a
cos(a-3π)*sin(3π/2+a)=-cosa * (-cosa)=cos²a
So sin 2 (a - π / 2) / cos (A-3 π) sin (3 π / 2 + a) = 1

Simplification of sin 2 θ - cos 2 θ

sin²θ-cos²θ
=-cos2θ

Simplification of sin α - cos α / sin? α + cos? α

∵sin²α+cos²α=1
The original formula = sin α - cos α

Simplification of sin 2 π / 16 cos 2 π / 16

-cosπ/8

Simplification √ 2 / 2 sin α + √ 2 / 2 cos α

√2/2 sinα+√2/2 cosα= sinαcosπ/4+√cosαsinπ/4=sin(α+π/4)

Simplification of sin (π / 2 + a) cos (π / 2-A) / cos (3 π / 2-A) sin (3 π / 2 + a) 2) sin25π/6+cos25π/3+tan(-25π/4)

sin(π/2+a)cos(π/2-a)/cos(3π/2-a)sin(3π/2+a)
=(cosasina)/(-sinα*-cosα)
=1
sin25π/6+cos25π/3+tan(-25π/4)
=sinπ/6+cosπ/3+tan(-π/4)
=1/2+1/2-1
=0
sin（2kπ+α）=sinα
cos（2kπ+α）=cosα
tan（2kπ+α）=tanα
cot（2kπ+α）=cotα
sec（2kπ+α）=secα
csc（2kπ+α）=cscα
sin（π+α）=－sinα
cos（π+α）=－cosα
tan（π+α）=tanα
cot（π+α）=cotα
sec(π+α)=-secα
csc(π+α)=-cscα
sin（－α）=－sinα
cos（－α）=cosα
tan（－α）=－tanα
cot（－α）=－cotα
sec(-α)=secα
csc(-α)=-cscα
sin（π－α）=sinα
cos（π－α）=-cosα
tan（π－α）=－tanα
cot（π－α）=－cotα
sec(π-α)=-secα
csc(π-α)=cscα
sin（α-π）=－sinα
cos（α-π）=－cosα
tan（α-π）=tanα
cot（α-π）=cotα
sec(α-π)=-secα
csc(α-π)=－cscα
sin（2π－α）=－sinα
cos（2π－α）=cosα
tan（2π－α）=－tanα
cot（2π－α）=－cotα
sec(2π-α)=secα
csc(2π-α)=-cscα
sin（π/2+α）=cosα
cos（π/2+α）=－sinα
tan（π/2+α）=－cotα
cot（π/2+α）=－tanα
sec(π/2+α)=-cscα
csc(π/2+α)=secα
sin（π/2－α）=cosα
cos（π/2－α）=sinα
tan（π/2－α）=cotα
cot（π/2－α）=tanα
sec(π/2-α)=cscα
csc(π/2-α)=secα
sin（3π/2+α）=－cosα
cos（3π/2+α）=sinα
tan（3π/2+α）=－cotα
cot（3π/2+α）=－tanα

Simplify cos ^ 4 (A / 2) - Sin ^ 4 (A / 2)

[cos(a/2)]^4-[sin(a/2)]^4
={[cos(a/2)]^2+[sin(a/2)]^2}×{[cos(a/2)]^2-[sin(a/2)]^2}
=1×{[cos(a/2)]^2-[sin(a/2)]^2}
=cos[2×(a/2)]
=cosa

Simplify sin a + cos a

Sin a + cos a = root 2 * (sin a * half root 2 + cos a * bisection root 2) = root 2 * (sin a * sin 45 ° + cos a * cos 45 °) - (1) = root 2 * cos (a-45 °) = root 2 * (sin a * cos 45 ° + cos a * sin 45 °) - (2) = root 2 * sin (a + 45 °)

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

sin(2π-a)=sin(-a)=-sina
cos(π+a)=-cosa
cos(π-a)=-cosa
sin(3π-a)=sina
sin(-π-a)=-sina
So the original formula = sinacosa / (cosasin? A)
=1/sina
=csca

Simplify cos (α - π / 2) / sin (α + 5 π / 2) * sin (α - 2 π) * cos (2 π - α), because I have just learned it, so I need the process of specific points Well The answer is the square of sin α

The original formula = (COS (- (π / 2 - α)) / sin (2 π + π / 2 + α)) * sin (- (2 π - α)) * cos (2 π - α)
=(cos(π/2-α)/sin(π/2+α))*(-sin(2π-α))*cosα
=(sinα/cosα)*sinα*cosα
=sin²α.