What is the value of (cos(pi/4))/(sin^2(pi/4)) ?

The value of (cos(pi/4))/(sin^2(pi/4)) is square root of 2

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(cos(pi/4))/(sin^2(pi/4))

\frac{cos ( \frac{π}{4} )}{sin ^{2} ( \frac{π}{4} )}

2

Solution steps

\frac{cos ( \frac{π}{4} )}{sin ^{2} ( \frac{π}{4} )}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

\frac{\frac{2}{2}}{( \frac{2}{2} ) ^{2}} : 2

= 2

4 sec (4 5^{\circ}) tan (4 5^{\circ})

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

sin (7 \cdot 0)

\frac{sin ( 1 )}{3}

sin (2 arccos (\frac{- 3}{5}))

What is the value of (cos(pi/4))/(sin^2(pi/4)) ?
The value of (cos(pi/4))/(sin^2(pi/4)) is square root of 2