Simplify cos(90 degrees -x)

Problem

cos(90−x)

Solution

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

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

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

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

cos(90−x)=(0)*cos(x)+(1)*sin(x)

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

cos(90−x)=0+sin(x)

cos(90−x)=sin(x)

Final Answer

cos(90−x)=sin(x)

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