Is cot(x)-sec(x)csc(x)cos(2x)=tan(x) ?

The answer to whether cot(x)-sec(x)csc(x)cos(2x)=tan(x) is True

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prove cot(x)-sec(x)csc(x)cos(2x)=tan(x)

prove

cot (x) - sec (x) csc (x) cos (2 x) = tan (x)

True

Solution steps

cot (x) - sec (x) csc (x) cos (2 x) = tan (x)

Manipulating left side

cot (x) - sec (x) csc (x) cos (2 x)

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

tan (x) = \frac{3}{7} = cos (x)

3 - 6 sin^{2} (x) = 3 sin (2 x)

sin (2 z) = sin (z) cos (z) + cos (z) sin (z)

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

\frac{( tan ( x ) cot ( x ) )}{cos ( x )} = sec (x)

Is cot(x)-sec(x)csc(x)cos(2x)=tan(x) ?
The answer to whether cot(x)-sec(x)csc(x)cos(2x)=tan(x) is True