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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= \frac{1}{sin ( x )}

Rewrite using trig identities

csc (x)

We showed that the two sides could take the same form

\Rightarrow True

1 + tan^{2} (- θ) = sec^{2} (θ)

\frac{tan ( x ) + tan ( y )}{cot ( x ) + cot ( y )} = tan (x) tan (y)

\frac{cos ( \frac{π}{2} + x )}{cos ( π + x )} = tan (x)

cot (x) sec (x) = csc (x)

1 - cos (2 x) = tan (x) sin (2 x)

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