Is (1+sec(x))(csc(x)-cot(x))=tan(x) ?

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

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prove (1+sec(x))(csc(x)-cot(x))=tan(x)

prove

(1 + sec (x)) (csc (x) - cot (x)) = tan (x)

True

Solution steps

(1 + sec (x)) (csc (x) - cot (x)) = tan (x)

Manipulating left side

(1 + sec (x)) (csc (x) - cot (x))

Express with sin, cos

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

2 - csc^{2} (z) = 1 - cot^{2} (z)

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

tan (t) sec (t) = \frac{sec ^{2} ( t ) - 1}{sin ( t )}

cos (2 x) = cos^{4} (x) - sin^{4} (x)

csc (\frac{π}{2} - u) = sec (u)

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