Simplify sin(90-x)

Problem

sin(90−x)

Solution

1. Identify the trigonometric identity for the sine of a difference of two angles.

2. Apply the formula sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B) where A=90 and B=x

sin(90−x)=sin(90)*cos(x)−cos(90)*sin(x)

3. Substitute the known values for sin(90) and cos(90) which are 1 and 0 respectively.

sin(90−x)=(1)*cos(x)−(0)*sin(x)

4. Simplify the expression by performing the multiplication and subtraction.

sin(90−x)=cos(x)

Final Answer

sin(90−x)=cos(x)

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