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Big problem of trigonometric function in senior three mathematics
1,SIN(x+ 10)+COS(x+40)= SIN(x+ 10)+SIN(x+ 130)= 2s in(x+70)COS 60。

In addition: y = sin (x+70-60)+cos (x+70-30).

= sin(x+70)/2-√3c OS(x+70)/2+√3c OS(x+70)/2+sin(x+70)/2

=sin(x+70)

2、T=8-2=6,ω=π/3

f(x)=Asin(πx/3+φ)

X=3 is the symmetry axis, and f(3)=Asin(π+φ)=A, so φ=-π/2.

f(x)=Asin(πx/3-π/2)

πx/3-π∈[2kπ-π/2,2kπ+π/2]

The solution is [6k+3/2, 6k+9/2], k ∈ z.