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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= sin (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ( 3 a ) cos ( 2 a )}{sin ( 3 a ) sin ( 2 a )} = \frac{cot ( 2 a )}{tan ( 3 a )}

\frac{1}{cos ^{2} ( θ )} = tan^{2} (θ) + 1

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

sin (b) cos^{2} (b) - sin (b) = - sin^{3} (b)

\frac{1}{2} (cot (θ) - tan (θ)) = cot (2 θ)

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