Answer
$$\sin x\tan x = \sin x\tan x$$
Work Step by Step
$$\eqalign{
& 2\sinh \left( {\ln \left( {\sec x} \right)} \right) = \sin x\tan x \cr
& {\text{definition of }}sinhx \cr
& 2\left( {\frac{{{e^{\ln \sec x}} - {e^{ - \ln \sec x}}}}{2}} \right) = \sin x\tan x \cr
& {\text{simplify}} \cr
& {e^{\ln \sec x}} - {e^{ - \ln \sec x}} = \sin x\tan x \cr
& \sec x - \frac{1}{{\sec x}} = \sin x\tan x \cr
& {\text{reciprocal identity}} \cr
& \frac{1}{{\cos x}} - \cos x = \sin x\tan x \cr
& \frac{{1 - {{\cos }^2}x}}{{\cos x}} = \sin x\tan x \cr
& {\text{identity si}}{{\text{n}}^2}x + {\cos ^2}x = 1 \cr
& \frac{{{{\sin }^2}x}}{{\cos x}} = \sin x\tan x \cr
& \sin x\frac{{\sin x}}{{\cos x}} = \sin x\tan x \cr
& \sin x\tan x = \sin x\tan x \cr} $$
