What is the value of tan(165) ?

The value of tan(165) is -2+sqrt(3)

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tan(165)

tan (16 5^{\circ})

- 2 + 3

Solution steps

tan (16 5^{\circ})

Rewrite using trig identities:

\frac{tan ( 10 5 ^{\circ} ) + tan ( 6 0 ^{\circ} )}{1 - tan ( 10 5 ^{\circ} ) tan ( 6 0 ^{\circ} )}

= \frac{tan ( 10 5 ^{\circ} ) + tan ( 6 0 ^{\circ} )}{1 - tan ( 10 5 ^{\circ} ) tan ( 6 0 ^{\circ} )}

Rewrite using trig identities:

tan (10 5^{\circ}) = - 2 - 3

Use the following trivial identity:

tan (6 0^{\circ}) = 3

= \frac{- 2 - 3 + 3}{1 - ( - 2 - 3 ) 3}

Simplify

\frac{- 2 - 3 + 3}{1 - ( - 2 - 3 ) 3} : - 2 + 3

= - 2 + 3

tan (\frac{1}{2})

cos (x) - sin (x) = 0, 0 \leq x \leq 2 π

cos (x) + 1 = sin (x)

tan (21 0^{\circ})

2 tan (θ) - sec^{2} (θ) = 0