What is the value of (tan(315))/(cot(420)) ?

The value of (tan(315))/(cot(420)) is -sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(tan(315))/(cot(420))

\frac{tan ( 31 5 ^{\circ} )}{cot ( 42 0 ^{\circ} )}

- 3

Solution steps

\frac{tan ( 31 5 ^{\circ} )}{cot ( 42 0 ^{\circ} )}

tan (31 5^{\circ}) = tan (13 5^{\circ})

= \frac{tan ( 13 5 ^{\circ} )}{cot ( 42 0 ^{\circ} )}

cot (42 0^{\circ}) = cot (6 0^{\circ})

= \frac{tan ( 13 5 ^{\circ} )}{cot ( 6 0 ^{\circ} )}

Rewrite using trig identities:

tan (13 5^{\circ}) = - 1

Use the following trivial identity:

cot (6 0^{\circ}) = \frac{3}{3}

= \frac{- 1}{\frac{3}{3}}

Simplify

\frac{- 1}{\frac{3}{3}} : - 3

= - 3

arctan (- \frac{1}{5})

arctan (- \frac{3}{1})

sec (arcsin (\frac{5}{13}))

sin (4 5^{\circ}) cos (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

sin^{2} (\frac{π}{12})

What is the value of (tan(315))/(cot(420)) ?
The value of (tan(315))/(cot(420)) is -sqrt(3)