What is the value of sin^2(30)-cot^2(60) ?

The value of sin^2(30)-cot^2(60) is -1/12

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sin^2(30)-cot^2(60)

sin^{2} (3 0^{\circ}) - cot^{2} (6 0^{\circ})

- \frac{1}{12}

Solution steps

sin^{2} (3 0^{\circ}) - cot^{2} (6 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

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

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

Simplify

(\frac{1}{2})^{2} - (\frac{3}{3})^{2} : - \frac{1}{12}

= - \frac{1}{12}

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

sin (\frac{6 π}{12})

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

arctan (2.90696 E 20)

cos (\frac{π}{2}) - sin (\frac{5 π}{3}) + tan (\frac{9 π}{4}) - cos (\frac{5 π}{6}) + tan (\frac{7 π}{6})

What is the value of sin^2(30)-cot^2(60) ?
The value of sin^2(30)-cot^2(60) is -1/12