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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

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

cos (\frac{π}{3}) = \frac{1}{2}

sec (- x) = sec (x)

cos (\frac{π}{3} + x) + cos (\frac{π}{3} - x) = cos (x)

sec^{2} (x) + tan^{2} (x) = 2 sec^{2} (x) - 1

cos^{2} (2 x) = \frac{1 + cos ( 4 x )}{2}

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