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

Problem

sin(π/2−x)*sec(x)

Solution

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

sin(π/2−x)=cos(x)

2. Substitute the identity back into the original expression.

cos(x)*sec(x)

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

cos(x)⋅1/cos(x)

4. Simplify the expression by canceling the common factor of cos(x)

1

Final Answer

sin(π/2−x)*sec(x)=1

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