Solve for x sin(x)sec(x)=tan(x)

Problem

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

Solution

1. Identify the trigonometric identity for the secant function, which is sec(x)=1/cos(x)

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

sin(x)⋅1/cos(x)=tan(x)

3. Simplify the left side by multiplying the terms.

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

4. Apply the quotient identity tan(x)=sin(x)/cos(x) to the left side.

tan(x)=tan(x)

5. Determine the domain of the equation. Since sec(x) and tan(x) are undefined when cos(x)=0 the equation holds for all x except where x=π/2+n*π for any integer n

Final Answer

sin(x)*sec(x)=tan(x)⇒x∈ℝ,x≠π/2+n*π

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