How do you evaluate $cos^-1 (-sqrt2/2)$ ?

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Answer 1 · 2018-06-26T13:22:27

$cos^-1(-sqrt2/2)=(3pi)/4$

Let ,

$A=cos^-1(-sqrt2/2)$

$=>A=cos^-1(-1/sqrt2)$

$=>A=pi-cos^-1(1/sqrt2)tocolor(red)([becausecos^-1(- x)$ = $color(red)(pi-cos^-1x)]$

$=>A=pi-cos^-1(cos(pi/4))...to[becausecolor(blue)(cos(pi/4)=1/sqrt2) ]$

$=>A=pi-pi/4$

$=>A=(3pi)/4$

How do you evaluate cos^-1 (-sqrt2/2)cos^-1 (-sqrt2/2)?