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

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

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

prove

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

True

Solution steps

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

Manipulating right side

\frac{cot ( x )}{sec ( x ) - tan ( x )}

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

1 + csc (x)

= csc (x) + 1

We showed that the two sides could take the same form

\Rightarrow True

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

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

sin (2 θ) = 2 cot (θ) sin^{2} (θ)

tan (θ) + 1 = sec (θ)

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

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