How do you find the value of $sec((5pi)/4)$ ?

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Answer 1 · 2018-04-06T09:19:40

$color(blue)(-sqrt(2))$

Identities:

$color(red)bb(secx=1/cosx) \ \ \ \ [1]$

$color(red)bb(cos(A+B)=cosAcosB-sinAsinB) \ \ \ [2]$

$cos((5pi)/4)=cos(pi+pi/4)$

Using $[2]$

$cos(pi+pi/4)=cos(pi)cos(pi/4)-sin(pi)sin(pi/4)$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =(-1)(sqrt(2)/2)-(0)((sqrt(2))/2)$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =-sqrt(2)/2$

Using $[1]$

$1/cosx\ \ \ \ \ \ \ \ \ \ \ \ =-1/(sqrt(2)/2)=-sqrt(2)$

$:.$

$color(blue)(sec((5pi)/4)=-sqrt(2))$

How do you find the value of sec((5pi)/4)sec((5pi)/4)?