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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(sec (u) - tan (u)) (csc (u) + 1)

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= cot (u)

We showed that the two sides could take the same form

\Rightarrow True

cot (2 θ) = \frac{csc ^{2} ( θ ) - 2}{2 cot ( θ )}

tan (θ + \frac{π}{4}) = \frac{1 + tan ( θ )}{1 - tan ( θ )}

tan (θ) = \frac{1}{cot ( θ )}

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

sin (x) = cos (x - \frac{π}{2})

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