Given Tan α = 3, find the square of (sin α + cos α). Given Tan α = - 1 / 3, find: 1 / 2 sin α cos α + cos square α

Given Tan α = 3, find the square of (sin α + cos α). Given Tan α = - 1 / 3, find: 1 / 2 sin α cos α + cos square α

(1) according to the universal formula: sin2 α = 2tan α / (1 + Tan ^ 2 α) = 3 / 5, so, (sin α + cos α) ^ 2 = 1 + sin2 α = 8 / 5; (2) because cos ^ 2 α = 1 / sec ^ 2 α = 1 / (1 + Tan ^ 2 α) = 9 / 10, 1 / 2sin2 α = Tan α / (1 + Tan ^ 2 α) = - (1 / 3) / (10 / 9) = - 3 / 10

If Tan α = 3, then sin square α - cos square α=

sin²α-cos²α
=(sin²α-cos²α)/1
=(sin²α-cos²α)/(sin²α+cos²α)
=(tan²α-1)/(tan²α+1)
=(9-1)/(9+1)
=4/5

It is known that sin (3 π + θ) = LG1 / (10 to the third power 0 {cos (π + θ) / cos θ [cos (π - θ) - 1]} + {cos (θ - π) / cos (π - θ) + cos (θ) It is known that sinlg (3 π) is open to the power of 10 Find {cos (π + θ) / cos θ [cos (π - θ) - 1]} + {cos (θ - 2 π) / cos (π - θ) + cos (θ - 2 π)] (the final result is 18)

The following is the: - sin θ = - 1 / 3; then cos ^ 2 θ = 8 / 9; then, cos (π + θ) / cos θ [cos (π - θ) - 1] - 9; the {cos (π + θ) / cos θ [cos (π - θ) - 1]} + {cos (π - 2 π) / cos (π - θ) + cos (θ - 2 π) + cos (θ - 2 π) has the following: - sin θ = - 1 / 3; then cos ^ 2 θ = 8 / 9; then cos ^ 2 θ = 8 / 9; {cos (π + θ) / cos θ [cos (π (π - θ) - 1]} the generation generation generation generation generation generation generation generation generation generation generation generation}} data, but feel like you

SiNx + cosx = m (absolute value of M

Let u = SiN x, v = cos x, then u + V = m, ① u ^ 2 + V ^ 2 = 1. ② from ① ^ 2 - ②, 2uv = m ^ 2 - 1, that is, UV = (m ^ 2 - 1) / 2

The derivation of Radix 2 [cos (X-B)] is equal to cosx + SiNx

According to the sum difference formula of two angles (COS (α - β) = cos α. Cos β + sin α. Sin β)
When B = π / 4
simple form
=√2[cos(X-π/4)]
=√2（cosXcosπ/4+sinXsinπ/4）
=√2（cosX*√2/2+sinX*√2/2）
=cosX+sinX

How to find the indefinite integral of SiNx to the power of 4 times the power of cosx?

The square of cosx is the square of 1-sinx. The n-th variance integral table (95) of SiNx can be found
Or Tongji textbook advanced mathematics volume I 220 pages

If sin α + SiNx + siny = 0, cos α + cosx + cosy = 0, then cos (X-Y) can find the process of thinking

Move the sine and cosine of X and y to the right of the equal sign respectively. The two formulas are squared at the same time and then added together. The left result is 1. When the right is expanded, you will find that it is equal to 1 1 1 (an expression), and the sum of that formula is required to be equal to - 1 / 2

Given sin (x + y) cosx cos (x-x) SiNx = 3 / 5, find the value of tan2y

It should be sin (x + y) cosx cos (x + y) SiNx = 3 / 5
sin[(x+y)-x]=3/5
siny=3/5
sin²y+cos²y=1
So cosy = ± 4 / 5
tany=siny/cosy=±3/4
tan2y=2tany/(1-tan²y)=(±3/2)/(7/16)
So tan2y = - 24 / 7 or 24 / 7

It is known that sin (π - x) - cos (π - x) = √ 2 / 3 (π / 2) (2) The value of (sin (2 π - x)) ^ 3 + (COS (2 π - x))

sin(π-x)-cos(π-x)=√2/3
SiNx + cosx = √ 2 / 3
(sinx+cosx)^2=(√2/3)^2=4/9=sinx^2+sinx^2+cosx^2+cosx^2
SiNx ^ 2 + cosx ^ 2 = 1
So 2sinxcosx = - 5 / 9
π/2

Given SiNx + cosx = 1 / 5 and 3 / 2 π < x < 2 π, find the value of 1 / (COS ^ 2x) - 1 / (sin ^ 2x)

[reference answer]
∵3π/2