What is the value of (tan((0.75pi)/2))/(tan((0.5pi)/2)) ?

The value of (tan((0.75pi)/2))/(tan((0.5pi)/2)) is sqrt(2)+1

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(tan((0.75pi)/2))/(tan((0.5pi)/2))

\frac{tan ( \frac{0.75 π}{2} )}{tan ( \frac{0.5 π}{2} )}

2 + 1

Solution steps

\frac{tan ( \frac{0.75 π}{2} )}{tan ( \frac{0.5 π}{2} )}

= \frac{tan ( \frac{\frac{3}{4} π}{2} )}{tan ( \frac{\frac{1}{2} π}{2} )}

Simplify:

\frac{\frac{3}{4} π}{2} = \frac{3 π}{8}

Simplify:

\frac{\frac{1}{2} π}{2} = \frac{π}{4}

= \frac{tan ( \frac{3 π}{8} )}{tan ( \frac{π}{4} )}

Rewrite using trig identities:

tan (\frac{3 π}{8}) = 3 + 22

Use the following trivial identity:

tan (\frac{π}{4}) = 1

= \frac{3 + 2 2}{1}

Simplify

\frac{3 + 2 2}{1} : 2 + 1

= 2 + 1

arccsch (2)

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sin (\frac{16 π}{1.4})

csc (1.5)

cos^{6} (\frac{π}{2})

What is the value of (tan((0.75pi)/2))/(tan((0.5pi)/2)) ?
The value of (tan((0.75pi)/2))/(tan((0.5pi)/2)) is sqrt(2)+1