Verify the Identity cos(x)sec(x)=1

Problem

cos(x)*sec(x)=1

Solution

1. Identify the trigonometric identity for the secant function.

2. Substitute the definition sec(x)=1/cos(x) into the left side of the equation.

cos(x)⋅1/cos(x)

3. Simplify the expression by canceling the common factor of cos(x) in the numerator and the denominator.

cos(x)/cos(x)=1

4. Conclude that the left side is equal to the right side, verifying the identity.

Final Answer

cos(x)*sec(x)=1

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