What is the value of (tan(315)-cos(780))/(tan(-135)-sin(210)) ?

The value of (tan(315)-cos(780))/(tan(-135)-sin(210)) is -1

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(tan(315)-cos(780))/(tan(-135)-sin(210))

\frac{tan ( 31 5 ^{\circ} ) - cos ( 78 0 ^{\circ} )}{tan ( - 13 5 ^{\circ} ) - sin ( 21 0 ^{\circ} )}

- 1

Solution steps

\frac{tan ( 31 5 ^{\circ} ) - cos ( 78 0 ^{\circ} )}{tan ( - 13 5 ^{\circ} ) - sin ( 21 0 ^{\circ} )}

Use the following property:

tan (- x) = - tan (x)

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

= \frac{tan ( 31 5 ^{\circ} ) - cos ( 78 0 ^{\circ} )}{- tan ( 13 5 ^{\circ} ) - sin ( 21 0 ^{\circ} )}

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

= \frac{tan ( 13 5 ^{\circ} ) - cos ( 78 0 ^{\circ} )}{- tan ( 13 5 ^{\circ} ) - sin ( 21 0 ^{\circ} )}

cos (78 0^{\circ}) = cos (6 0^{\circ})

= \frac{tan ( 13 5 ^{\circ} ) - cos ( 6 0 ^{\circ} )}{- tan ( 13 5 ^{\circ} ) - sin ( 21 0 ^{\circ} )}

Rewrite using trig identities:

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

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Rewrite using trig identities:

sin (21 0^{\circ}) = - \frac{1}{2}

= \frac{- 1 - \frac{1}{2}}{- ( - 1 ) - ( - \frac{1}{2} )}

Simplify

\frac{- 1 - \frac{1}{2}}{- ( - 1 ) - ( - \frac{1}{2} )} : - 1

= - 1

2 - 2 cosh (3 - 2)

arctan (0.99)

arctan (\frac{- 6}{3})

arctan (- \frac{7}{6})

arccos (\frac{10}{3})

What is the value of (tan(315)-cos(780))/(tan(-135)-sin(210)) ?
The value of (tan(315)-cos(780))/(tan(-135)-sin(210)) is -1