What is the value of (1+cot^2(30))/(1+tan^2(30)) ?

The value of (1+cot^2(30))/(1+tan^2(30)) is 3

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(1+cot^2(30))/(1+tan^2(30))

\frac{1 + cot ^{2} ( 3 0 ^{\circ} )}{1 + tan ^{2} ( 3 0 ^{\circ} )}

3

Solution steps

\frac{1 + cot ^{2} ( 3 0 ^{\circ} )}{1 + tan ^{2} ( 3 0 ^{\circ} )}

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

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

= 3

arctan (\frac{8}{- 4})

1 + tan^{2} (3 0^{\circ}) - csc^{2} (4 5^{\circ})

cos (2 \cdot 2 π)

- tan (\frac{3}{3})

cos (- \frac{7 π}{8})

What is the value of (1+cot^2(30))/(1+tan^2(30)) ?
The value of (1+cot^2(30))/(1+tan^2(30)) is 3