What is the value of 500sec^2(arctan(1/2))(12pi) ?

The value of 500sec^2(arctan(1/2))(12pi) is 7500pi

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500sec^2(arctan(1/2))(12pi)

500 sec^{2} (arctan (\frac{1}{2})) (12 π)

7500 π

Solution steps

500 sec^{2} (arctan (\frac{1}{2})) (12 π)

= 500 sec^{2} (arctan (\frac{1}{2})) \cdot 12 π

Rewrite using trig identities:

sec (arctan (\frac{1}{2})) = \frac{5}{2}

= 500 (\frac{5}{2})^{2} \cdot 12 π

Simplify

500 (\frac{5}{2})^{2} \cdot 12 π : 7500 π

= 7500 π

sin (arccos (\frac{5}{13}))

cos (\frac{5 π}{12}) cos (\frac{π}{4}) + sin (\frac{5 π}{12}) sin (\frac{π}{4})

sec (- \frac{11 π}{6})

arctan (\frac{13}{9})

\frac{1}{sin ( \frac{π}{2} )}

What is the value of 500sec^2(arctan(1/2))(12pi) ?
The value of 500sec^2(arctan(1/2))(12pi) is 7500pi