Given Tan θ / 2 = 1 / 4, find sin θ + cos θ,

Given Tan θ / 2 = 1 / 4, find sin θ + cos θ,

Using the angle doubling formula Tan θ = [2tan (θ / 2)] / [1 - (Tan θ / 2) ^ 2] = 8 / 15, then Tan θ = sin θ / cos θ = 8 / 15, (sin θ) ^ 2 + (COS θ) ^ 2 = 1, we can get sin θ and cos θ, and finally sin θ + cos θ

Given sin α = 8 / 17, cos β = - 5 / 13, α, β ∈ (π / 2, π), find the value of COS (α + β)

α∈(π/2,π),
So cos α 0
(sinβ)^2+(cosβ)^2=0
cosβ=-5/13
So sin β = 12 / 13
cos(α+β)=cosαcosβ-sinαsinβ
=(-15/17)*(-5/13)-(8/17)*(12/13)
=-21/221

What is (COS ^ 2) 15 ° - (sin ^ 2) 15

This is because: Method 1: (COS ^ 2) 15 ° - (sin ^ 2) 15 = (cos15 + sin15) (cos15-sin15) = [sin (90-15) + sin15] [sin (90-15) - sin15] = (sin75 + sin15) (sin75-sin15) = 2 * sin (75 + 15) / 2 * cos (75-15) / 2 * 2 * cos (75 + 15) * sin (75-15) / 2 = 4 * sin45 * cos30 * cos

What is (COS ^ 2) 15 ° + (sin ^ 2) 15 ° equal to

1 formula (COS ^ 2) x + (sin ^ 2) x = 1

Sin α = 15 / 17. α∈ (π / 2, π) for cos (π / 3 - α)

∵α∈(π/2,π)
∴cosα

If sin θ + sin ^ 2 θ = 1, then cos ^ 2 θ + cos ^ 4 θ + cos ^ 6 θ

Sin θ + sin ^ 2 θ = 1, sin ^ 2 θ + cos ^ 2 θ = 1 ｛ sin θ = cos ^ 2 θ both sides of the equation multiply sin θ at the same time. There are sin ^ 2 θ + sin ^ 3 θ = sin θ ｛ sin ^ 3 θ = sin θ - Sin ^ 2 θ = cos ^ 2 θ - Sin ^ 2 θ = cos 2 θ ｛ sin θ + sin ^ 2 θ + sin ^ 3 θ = 1 + sin ^ 3 θ = 1 + cos ^ 2 θ = 2 sin θ roots

If sin ^ 2 α + sin α = 1, then cos ^ 4 α + cos ^ 2 α=

(sina)^2+sina=1
(sina)^2=1-sina
(cosa)^2=1-(sina)^2=1-1+sina=sina
(cosa)^4=(sina)^2
(cosa)^4+(cosa)^2=(sina)^2+sina=1

sin(π+π/6)-cos(π+π/4)cos(-π/2)+1
evaluation

sin(π+π/6)-cos(π+π/4)cos(-π/2)+1
=-sin(π/6)+cos(π/4)cos(+π/2)+1
=-1/2+cos(π/4)*0+1
=1/2

Evaluation: Tan 675 ° + cos 675 ° - sin (- 5 π - 2) + 1 / cos (- 17 π - 3)=

tan675°+cos675°-sin(-5π/2)+1/cos(-17π/3)
=tan(720°-45°)+cos(720°-45°)-sin(-5π/2+2π)+1/cos(-17π/3+6π)
=-tan45°+cos45°-sin(-π/2)+1/cos(π/3)
=-tan45°+cos45°+sin(π/2)+1/cos(π/3)
=-1+√2/2+1+1/(1/2)
=√2/2+2

Evaluation of sin (α + 4 π) cos (α - 4 π) - cos (α + 4 π) sin (α - 4 π)

Directly use the sine formula of the sum of two angles
sin(α+π/4)cos(α-π/4)-cos(α+π/4)sin(α-π/4)
=sin[(α+π/4)-(α-π/4)]
=sin(α+π/4-α+π/4)
=sin(π/2)
=1