The value of the expression Csc(6x)-cot(6x)/csc(6x)+cot(6x) is tan²3x.
Trigonometric Ratios are ratios of the side of a right angled triangle. These are used to find the missing sides and angles of a right angled triangle.
[tex]\rm =\dfrac {cosine(6x)-cot(6x)}{cosine(6x)+cot(6x)}\\\\\\\ = \dfrac{ \dfrac{1}{sin6x} - \dfrac{cos6x}{sin6x}}{ \dfrac{1}{sin6x} + \dfrac{cos6x}{sin6x}}\\\\\\ = \dfrac{ 1-cos 6x}{1+cos6x}[/tex]
( 1- cosx = 2sin²x/2) ( 1+cosx = 2cos²x/2)
[tex]\rm = \dfrac{ 2 sin^2 3x}{2 cos^2 3x}\\\\\\\\=tan^2 3x[/tex]
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