Simplification: the fourth power of sin, the square of COS, the square of sin and the square of COS=

Simplification: the fourth power of sin, the square of COS, the square of sin and the square of COS=

(sinθ)^4+(cosθ)^2+(sinθ)^2(cosθ)^2
=((1-cos2θ)/2)^2+(cosθ)^2+(sin2θ/2)^2
=1/4-cos2θ/2+cos(2θ)^2/4+(1+cos2θ)/2+(sin2θ)^2/4
=1/4+1/4+1/2=1

The fourth power of sin + the fourth power of COS a = 1-2sin, how to simplify the square a of ACOS?

The original formula = (the square of sin α + the square of cos α) - 4 the square of sin α * the square of cos α
=The square of 1-4sin α * cos α
=The square of 1 - (2Sin α * cos α)
=The square of 1-2 sin2 α = Cos4 α

Cos quartic α - Sin quartic α reduction

cos^4a-sin^4a^=(cos^2+sin^2)(cos^2a-sin^2a)=cos^2a-sin^2a=cos2a

Simplification: (1) the third power of Tan (2 π + α) Tan (π + α) cos (- π - α) is the square of sin (- α) multiplied by cos (π + α); (2) Cos (π - α) Tan (3 π - α), sin (2 π - α) Tan (π + α)

(1) the original formula = [(- Sina) ^ 2 * (- COSA)] / [Tana * Tana * (- COSA) ^ 3]
=sin^2a/(tan^2a*cos^2a)
=sin^2a/sin^2a
=1；
(2) the original formula = [(- Sina) * Tana] / (- COSA) * [(- Tana)]
=-sina/cosa
=-tana.

It is proved that (1) sin quartic α + sin? α co? α + cos? α = 1 (2) sin quartic α - cos? α = sin? α - cos? α

(1) Sin quartic α + sin? α co? α + cos? α = 1? Left = sin? α (sin? α + cos? α) + cos? α = sin? 2A + cos? α = 1? Right = 1? Sin? Quartic α + sin? α? Co? α + cos? α

Simplification: sin quartic α + sin? α * cos? α + cos? α

The original formula = sin? α (sin? α + cos? α) + cos? α
=sin²α*1+cos²α
=sin²α+cos²α
=1

If the square of sin a + Sina = 1, then the fourth power of COS a + the square of COS a =?

Hello!
sin²a+sina=1 , sina=1-sin²a=cos²a
cos⁴a+cos²a=sin²a+sina=1

We know that sina + sin? A = 1. Solve the fourth power of cos? A + cosa + the eighth power of cosa!

Wait a minute. It's more difficult to type

The fourth power of (COS π / 8) is equal to the fourth power of - (sin π / 8)

The fourth power of (COS π / 8) - (sin π / 8) = (COS 2 (π / 8) - Sin 2 (π / 8)) (COS 2 (π / 8) + sin 2 (π / 8)) = cos 2 (π / 8) - Sin 2 (π / 8). The formula of sum of squares (COS 2 (π / 8) + sin 2 (π / 8)) = 1 = cos (π / 4)

How to calculate the fourth power of sin minus the fourth power of COS, especially the step to get the number

The original formula = - (COS? A + sin? A) (COS? A-SiN? A)
=-1*cos2a
=-cos2a