Simplify cos(pi/2-x)sec(x)

Problem

cos(π/2−x)*sec(x)

Solution

1. Apply the cofunction identity for the cosine function, which states that cos(π/2−x)=sin(x)

2. Substitute the identity into the original expression.

sin(x)*sec(x)

3. Use the reciprocal identity for the secant function, where sec(x)=1/cos(x)

sin(x)⋅1/cos(x)

4. Combine the terms into a single fraction.

sin(x)/cos(x)

5. Apply the quotient identity for the tangent function, which states that sin(x)/cos(x)=tan(x)

Final Answer

cos(π/2−x)*sec(x)=tan(x)

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