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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= cot (a)

We showed that the two sides could take the same form

\Rightarrow True

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

(cot (x) + tan (x))^{2} = sec^{2} (x) csc^{2} (x)

6 sin (\frac{5 π}{6}) = 2 + 2 sin (\frac{5 π}{6})

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

\frac{0}{sin ( x ) cos ( x )} = 0

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