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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (A)

We showed that the two sides could take the same form

\Rightarrow True

- sin (x) = cos (\frac{π}{2} + x)

sin (a + b) - sin (a - b) = 2 cos (a) sin (b)

1 + cot^{2} (θ) = \frac{1}{sin ^{2} ( θ )}

sin (2 π - x) = - sin (x)

csc (θ) - \frac{sin ( θ )}{1 + cos ( θ )} = cot (θ)

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