Is csc(x)-cot(x)cos(x)= 1/(csc(x)) ?

The answer to whether csc(x)-cot(x)cos(x)= 1/(csc(x)) is True

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prove csc(x)-cot(x)cos(x)= 1/(csc(x))

prove

csc (x) - cot (x) cos (x) = \frac{1}{csc ( x )}

True

Solution steps

csc (x) - cot (x) cos (x) = \frac{1}{csc ( x )}

Manipulating left side

csc (x) - cot (x) cos (x)

Express with sin, cos

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

Rewrite using trig identities

= sin (x)

Use the basic trigonometric identity:

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

= \frac{1}{csc ( x )}

We showed that the two sides could take the same form

\Rightarrow True

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

csc (Θ) + sin (- Θ) = \frac{cos ^{2} ( Θ )}{sin ( Θ )}

cos (4 x) = cos^{2} (2 x) + sin^{2} (2 x)

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

csc (A) = \frac{cos ( 2 A )}{sin ( A )} + \frac{sin ( 2 A )}{cos ( A )}

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