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

The value of tan^2(30)+csc^2(60) is 5/3

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

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

\frac{5}{3}

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

(\frac{3}{3})^{2} + (\frac{2 3}{3})^{2} : \frac{5}{3}

= \frac{5}{3}

10 \cdot csc (2 3^{\circ})

arcsin (sin (\frac{5 π}{12}))

(cos (\frac{2 π}{3}) + i sin (\frac{2 π}{3}))^{2}

csc (25 5^{\circ})

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

What is the value of tan^2(30)+csc^2(60) ?
The value of tan^2(30)+csc^2(60) is 5/3