Is (tan(2x))/(1+sec(2x))=tan(x) ?

The answer to whether (tan(2x))/(1+sec(2x))=tan(x) is True

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prove (tan(2x))/(1+sec(2x))=tan(x)

prove

\frac{tan ( 2 x )}{1 + sec ( 2 x )} = tan (x)

True

Solution steps

\frac{tan ( 2 x )}{1 + sec ( 2 x )} = tan (x)

Manipulating left side

\frac{tan ( 2 x )}{1 + sec ( 2 x )}

Express with sin, cos

= \frac{sin ( 2 x )}{1 + cos ( 2 x )}

Rewrite using trig identities

= \frac{sin ( x )}{cos ( x )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) - cos^{2} (x) = sin (x)

tan (\frac{π}{2} - θ) sin (θ) = cos (θ)

sin (\frac{5 π}{3}) = - \frac{3}{2}

\frac{sec ( y )}{sec ( y ) - cos ( y )} = csc^{2} (y)

sin^{2} (x) + 4 sin (x) + 4 = (sin (x) + 2)^{2}

Is (tan(2x))/(1+sec(2x))=tan(x) ?
The answer to whether (tan(2x))/(1+sec(2x))=tan(x) is True