Is (csc(6x)+cot(6x))/(csc(6x)-cot(6x))=tan(6x) ?

The answer to whether (csc(6x)+cot(6x))/(csc(6x)-cot(6x))=tan(6x) is False

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prove (csc(6x)+cot(6x))/(csc(6x)-cot(6x))=tan(6x)

prove

\frac{csc ( 6 x ) + cot ( 6 x )}{csc ( 6 x ) - cot ( 6 x )} = tan (6 x)

False

Solution steps

\frac{csc ( 6 x ) + cot ( 6 x )}{csc ( 6 x ) - cot ( 6 x )} = tan (6 x)

Show that the two sides are not equal

For

\frac{csc ( 6 x ) + cot ( 6 x )}{csc ( 6 x ) - cot ( 6 x )} = tan (6 x)

plug in

x = 1

\frac{csc ( 6 \cdot 1 ) + cot ( 6 \cdot 1 )}{csc ( 6 \cdot 1 ) - cot ( 6 \cdot 1 )} = 49.21376 \dots

\frac{csc ( 6 \cdot 1 ) + cot ( 6 \cdot 1 )}{csc ( 6 \cdot 1 ) - cot ( 6 \cdot 1 )}

Refine to a decimal form

= 49.21376 \dots

tan (6 \cdot 1) = - 0.29100 \dots

tan (6 \cdot 1)

Refine to a decimal form

= - 0.29100 \dots

The two sides are not equal

\Rightarrow False

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

csc^{4} (x) - cot^{4} (x) = 1 + 2 cot^{2} (x)

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

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

csc (A) - sin (A) = cot (A) cos (A)

Is (csc(6x)+cot(6x))/(csc(6x)-cot(6x))=tan(6x) ?
The answer to whether (csc(6x)+cot(6x))/(csc(6x)-cot(6x))=tan(6x) is False