Is csc^2(x)-1=(cos(x))/(tan(x)sin(x)) ?

The answer to whether csc^2(x)-1=(cos(x))/(tan(x)sin(x)) is True

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prove csc^2(x)-1=(cos(x))/(tan(x)sin(x))

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

csc^{2} (x) - 1

We showed that the two sides could take the same form

\Rightarrow True

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

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

2 cos^{2} (x) = 0

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

sec^{2} (A) - cos (A) sec (A) = tan^{2} (A)

Is csc^2(x)-1=(cos(x))/(tan(x)sin(x)) ?
The answer to whether csc^2(x)-1=(cos(x))/(tan(x)sin(x)) is True