Simplify

Problem

cos2(π/2−x)/√(,1−sin2(x))

Solution

1. Apply the co-function identity to the numerator using the relation cos(π/2−x)=sin(x)

cos2(π/2−x)=sin2(x)

2. Apply the Pythagorean identity to the expression inside the square root in the denominator using 1−sin2(x)=cos2(x)

√(,1−sin2(x))=√(,cos2(x))

3. Simplify the square root by assuming the standard principal value or absolute value, though in basic simplification it is often expressed as cos(x)

√(,cos2(x))=cos(x)

4. Combine the results to form the simplified fraction.

sin2(x)/cos(x)

5. Rewrite using trigonometric identities by separating the terms into sin(x)⋅sin(x)/cos(x)

sin(x)⋅tan(x)

Final Answer

cos2(π/2−x)/√(,1−sin2(x))=sin(x)*tan(x)

Want more problems? Check here!