What is the value of sin^2(60)+tan^2(60)-csc^2(30) ?

The value of sin^2(60)+tan^2(60)-csc^2(30) is -1/4

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sin^2(60)+tan^2(60)-csc^2(30)

sin^{2} (6 0^{\circ}) + tan^{2} (6 0^{\circ}) - csc^{2} (3 0^{\circ})

- \frac{1}{4}

Solution steps

sin^{2} (6 0^{\circ}) + tan^{2} (6 0^{\circ}) - csc^{2} (3 0^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

csc (3 0^{\circ}) = 2

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

Simplify

(\frac{3}{2})^{2} + (3)^{2} - 2^{2} : - \frac{1}{4}

= - \frac{1}{4}

(875)^{3} - sin (87 5^{\circ})

\frac{sin ( \frac{π}{6} )}{cos ( \frac{π}{6} )}

cos (arccos (\frac{π}{2}))

tan (- 40 5^{\circ})

arccosh (3)

What is the value of sin^2(60)+tan^2(60)-csc^2(30) ?
The value of sin^2(60)+tan^2(60)-csc^2(30) is -1/4