Is tan(x)=cot(x)-2cot(2x) ?

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

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prove tan(x)=cot(x)-2cot(2x)

prove

tan (x) = cot (x) - 2 cot (2 x)

True

Solution steps

tan (x) = cot (x) - 2 cot (2 x)

Manipulating right side

cot (x) - 2 cot (2 x)

Express with sin, cos

= \frac{cos ( x ) sin ( 2 x ) - 2 cos ( 2 x ) sin ( x )}{sin ( 2 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 (3 x) (tan (x) - 1) = 0

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

csc^{2} (x) - cot^{2} (x) + 1 = 0

cos (- b) tan (b) csc (b) cot (b) = cot (b)

cos (2 x) = sin (2 x) cos (2 x) + cos (4 x)

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