cosx-sinx

=√(cosxcos45 -sinxsin45)

=√cos(x+45)

Sinks-Kosks

=√(sinxcos45 -cosxsin45)

=√sin(x-45)

Extended data

Trigonometric function is one of the basic elementary functions, which takes the angle (the most commonly used radian system in mathematics, the same below) as the independent variable, and the angle corresponds to the coordinates where the terminal edge of any angle intersects with the unit circle or its ratio as the dependent variable.

Common trigonometric functions are sine function, cosine function and tangent function. Other trigonometric functions, such as cotangent function, secant function, cotangent function, dyadic function, cofactor function, semidyadic function and semifactorial function, are also used in other disciplines, such as navigation, surveying and engineering. The relationship between different trigonometric functions can be obtained by geometric intuition or calculation, which is called trigonometric identity.

Reference source

Baidu Encyclopedia-formulas of trigonometric functions