What is the value of (tan(17)-cot(73))/(cot(17)) ?

The value of (tan(17)-cot(73))/(cot(17)) is 0

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(tan(17)-cot(73))/(cot(17))

\frac{tan ( 1 7 ^{\circ} ) - cot ( 7 3 ^{\circ} )}{cot ( 1 7 ^{\circ} )}

0

Solution steps

\frac{tan ( 1 7 ^{\circ} ) - cot ( 7 3 ^{\circ} )}{cot ( 1 7 ^{\circ} )}

Rewrite using trig identities:

tan (1 7^{\circ}) = cot (7 3^{\circ})

tan (1 7^{\circ})

Use the following identity:

tan (x) = cot (9 0^{\circ} - x)

cot (9 0^{\circ} - x)

Use the basic trigonometric identity:

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

= \frac{cos ( 9 0 ^{\circ} - x )}{sin ( 9 0 ^{\circ} - x )}

Use the Angle Difference identity:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= \frac{cos ( 9 0 ^{\circ} ) cos ( x ) + sin ( 9 0 ^{\circ} ) sin ( x )}{sin ( 9 0 ^{\circ} - x )}

Use the Angle Difference identity:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= \frac{cos ( 9 0 ^{\circ} ) cos ( x ) + sin ( 9 0 ^{\circ} ) sin ( x )}{sin ( 9 0 ^{\circ} ) cos ( x ) - cos ( 9 0 ^{\circ} ) sin ( x )}

Use the following trivial identity:

cos (9 0^{\circ}) = 0

Use the following trivial identity:

sin (9 0^{\circ}) = 1

= \frac{0 cos ( x ) + 1 sin ( x )}{1 cos ( x ) - 0 sin ( x )}

Simplify

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

Use the basic trigonometric identity:

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

= tan (x)

= cot (9 0^{\circ} - 1 7^{\circ})

Simplify

= cot (7 3^{\circ})

= \frac{cot ( 7 3 ^{\circ} ) - cot ( 7 3 ^{\circ} )}{cot ( 1 7 ^{\circ} )}

Simplify

= 0

6 sin (27 0^{\circ})

6 (cos (15 0^{\circ}) + i sin (15 0^{\circ}))

arcsin (\frac{2}{11})

2 - 4 cos (\frac{3 π}{2})

ln tan (\frac{π}{3}) + sec (π^{3})

What is the value of (tan(17)-cot(73))/(cot(17)) ?
The value of (tan(17)-cot(73))/(cot(17)) is 0