=√2(√2/2sinx+√2/2cosx)

=√2(sinxcos45+cosxsin45)

=√2sin(x+45).

The meaning of the inductive formula "odd and even changes, the sign depends on the quadrant";

Trigonometric function value of k× π/2 A (k ∈ z).

(1) When k is an even number, it is equal to the trigonometric function value of the same name of α, preceded by a sign of the original trigonometric function value when α is regarded as an acute angle.

(2) When k is an odd number, different trigonometric function values equal to α are preceded by a sign of the original trigonometric function value when α is regarded as an acute angle.

The six angles of a hexagon represent six kinds of trigonometric functions respectively, and they are related as follows:

1) The diagonal product is 1, that is, sinθ cscθ =1; cosθsecθ= 1； tanθ cotθ= 1 .

2) A trigonometric function represented by any three adjacent vertices of a hexagon, and the function value in the middle position is equal to the product of two adjacent function values, such as: sin θ = cos θ tan θ; tanθ=sinθ secθ.

3) For the triangle in the shaded part, the sum of squares of the top two vertices is equal to the square value of the bottom vertex.