What is the value of (tan(35))/(cot(55)) ?

The value of (tan(35))/(cot(55)) is 1

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(tan(35))/(cot(55))

\frac{tan ( 3 5 ^{\circ} )}{cot ( 5 5 ^{\circ} )}

1

Solution steps

\frac{tan ( 3 5 ^{\circ} )}{cot ( 5 5 ^{\circ} )}

Rewrite using trig identities:

tan (3 5^{\circ}) = cot (5 5^{\circ})

tan (3 5^{\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} - 3 5^{\circ})

Simplify

= cot (5 5^{\circ})

= \frac{cot ( 5 5 ^{\circ} )}{cot ( 5 5 ^{\circ} )}

Simplify

= 1

\frac{4}{3} cos (13 5^{\circ})

tan (5 8^{\circ}) \cdot 2

arctan (1.92)

sec (\frac{155 π}{2})

- arctan (2 \cdot 0.83 \cdot 1 0^{8} \cdot 10 \cdot 1 0^{- 9} (12))

What is the value of (tan(35))/(cot(55)) ?
The value of (tan(35))/(cot(55)) is 1