What is the value of (1+sec(60)cot(60))/(1-tan(30)sec(30)) ?

The value of (1+sec(60)cot(60))/(1-tan(30)sec(30)) is 3+2sqrt(3)

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(1+sec(60)cot(60))/(1-tan(30)sec(30))

\frac{1 + sec ( 6 0 ^{\circ} ) cot ( 6 0 ^{\circ} )}{1 - tan ( 3 0 ^{\circ} ) sec ( 3 0 ^{\circ} )}

3 + 23

Solution steps

\frac{1 + sec ( 6 0 ^{\circ} ) cot ( 6 0 ^{\circ} )}{1 - tan ( 3 0 ^{\circ} ) sec ( 3 0 ^{\circ} )}

Use the following trivial identity:

sec (6 0^{\circ}) = 2

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

sec (3 0^{\circ}) = \frac{2 3}{3}

= \frac{1 + 2 \cdot \frac{3}{3}}{1 - \frac{3}{3} \cdot \frac{2 3}{3}}

Simplify

\frac{1 + 2 \cdot \frac{3}{3}}{1 - \frac{3}{3} \cdot \frac{2 3}{3}} : 3 + 23

= 3 + 23

sin (16 8^{\circ})

arctan (\frac{100}{300})

60 \cdot sin (2 0^{\circ})

arctan (- 26)

\frac{sin ^{2} ( \frac{π}{4} )}{tan ^{3} ( \frac{π}{4} )}

What is the value of (1+sec(60)cot(60))/(1-tan(30)sec(30)) ?
The value of (1+sec(60)cot(60))/(1-tan(30)sec(30)) is 3+2sqrt(3)