What is the value of sec^2(pi/4)+4csc^2(pi/3) ?

The value of sec^2(pi/4)+4csc^2(pi/3) is 22/3

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sec^2(pi/4)+4csc^2(pi/3)

sec^{2} (\frac{π}{4}) + 4 csc^{2} (\frac{π}{3})

\frac{22}{3}

Solution steps

sec^{2} (\frac{π}{4}) + 4 csc^{2} (\frac{π}{3})

Use the following trivial identity:

sec (\frac{π}{4}) = 2

Use the following trivial identity:

csc (\frac{π}{3}) = \frac{2 3}{3}

= (2)^{2} + 4 (\frac{2 3}{3})^{2}

Simplify

(2)^{2} + 4 (\frac{2 3}{3})^{2} : \frac{22}{3}

= \frac{22}{3}

sin (3 0^{\circ}) + (sin (4 5^{\circ})) (sin (4 5^{\circ})) - 1

2 \cdot 9.81 \cdot 3.5 \cdot cos (5 0^{\circ})

sin (25 0^{\circ}) cos (1 0^{\circ}) - cos (25 0^{\circ}) sin (1 0^{\circ})

arctan (\frac{- 2}{2})

csc (8 3^{\circ})

What is the value of sec^2(pi/4)+4csc^2(pi/3) ?
The value of sec^2(pi/4)+4csc^2(pi/3) is 22/3