What is the value of tan(37.5) ?

The value of tan(37.5) is sqrt((4-\sqrt{6)+sqrt(2))/(4+sqrt(6)-\sqrt{2)}}

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tan(37.5)

tan (37. 5^{\circ})

\frac{4 - 6 + 2}{4 + 6 - 2}

Solution steps

tan (37. 5^{\circ})

Rewrite using trig identities:

\frac{1 - cos ( 7 5 ^{\circ} )}{1 + cos ( 7 5 ^{\circ} )}

= \frac{1 - cos ( 7 5 ^{\circ} )}{1 + cos ( 7 5 ^{\circ} )}

Rewrite using trig identities:

cos (7 5^{\circ}) = \frac{6 - 2}{4}

= \frac{1 - \frac{6 - 2}{4}}{1 + \frac{6 - 2}{4}}

Simplify

\frac{1 - \frac{6 - 2}{4}}{1 + \frac{6 - 2}{4}} : \frac{4 - 6 + 2}{4 + 6 - 2}

= \frac{4 - 6 + 2}{4 + 6 - 2}

\frac{2}{cos ( 2 0 ^{\circ} )}

44 sin (4 5^{\circ})

60 \cdot cos (3 7^{\circ})

- 2 cos (- \frac{π}{7})

45 sin (7 0^{\circ})

What is the value of tan(37.5) ?
The value of tan(37.5) is sqrt((4-\sqrt{6)+sqrt(2))/(4+sqrt(6)-\sqrt{2)}}