What is the value of (tan(-(2pi)/3))/(sin((7pi)/4))-sec(-pi) ?

The value of (tan(-(2pi)/3))/(sin((7pi)/4))-sec(-pi) is -sqrt(6)+1

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(tan(-(2pi)/3))/(sin((7pi)/4))-sec(-pi)

\frac{tan ( - \frac{2 π}{3} )}{sin ( \frac{7 π}{4} )} - sec (- π)

- 6 + 1

Solution steps

\frac{tan ( - \frac{2 π}{3} )}{sin ( \frac{7 π}{4} )} - sec (- π)

\frac{tan ( - \frac{2 π}{3} )}{sin ( \frac{7 π}{4} )} - sec (- π) = \frac{tan ( - \frac{2 π}{3} ) - sec ( - π ) sin ( \frac{7 π}{4} )}{sin ( \frac{7 π}{4} )}

= \frac{tan ( - \frac{2 π}{3} ) - sec ( - π ) sin ( \frac{7 π}{4} )}{sin ( \frac{7 π}{4} )}

Use the following property:

sec (- x) = sec (x)

sec (- π) = sec (π)

= \frac{tan ( - \frac{2 π}{3} ) - sec ( π ) sin ( \frac{7 π}{4} )}{sin ( \frac{7 π}{4} )}

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{2 π}{3}) = - tan (\frac{2 π}{3})

= \frac{- tan ( \frac{2 π}{3} ) - sec ( π ) sin ( \frac{7 π}{4} )}{sin ( \frac{7 π}{4} )}

Rewrite using trig identities:

tan (\frac{2 π}{3}) = - 3

Use the following trivial identity:

sec (π) = (- 1)

Rewrite using trig identities:

sin (\frac{7 π}{4}) = - \frac{2}{2}

= \frac{- ( - 3 ) - ( - 1 ) ( - \frac{2}{2} )}{- \frac{2}{2}}

Simplify

\frac{- ( - 3 ) - ( - 1 ) ( - \frac{2}{2} )}{- \frac{2}{2}} : - 6 + 1

= - 6 + 1

tan (- \frac{5 π}{8})

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

arcsin (0.82)

arcsin (0.78)

arcsin (0.76)

What is the value of (tan(-(2pi)/3))/(sin((7pi)/4))-sec(-pi) ?
The value of (tan(-(2pi)/3))/(sin((7pi)/4))-sec(-pi) is -sqrt(6)+1