Verify the Identity sin(x)*sec(x)=tan(x)

Problem

sin(x)*sec(x)=tan(x)

Solution

1. Identify the trigonometric identity for the secant function.

sec(x)=1/cos(x)

2. Substitute the identity into the left side of the equation.

sin(x)⋅1/cos(x)

3. Multiply the terms to combine them into a single fraction.

sin(x)/cos(x)

4. Apply the quotient identity for the tangent function.

sin(x)/cos(x)=tan(x)

Final Answer

sin(x)*sec(x)=tan(x)

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