How do you solve #csc[tan^-1 (-2)] #?

1 Answer
Shwetank Mauria
Dec 3, 2016

#csc(tan^(-1)(-2))=-sqrt5/2#

Explanation:

From the definition of inverse ratios, if #tan^(-1)(-2)=theta#, then #tantheta=-2#

As #tantheta=-2#, we have #cottheta=-1/2# and

#csctheta=-sqrt(1+(-1/2)^2)=-sqrt(1+1/4)#

= #-sqrt(5/4)=-sqrt5/2#

Note that as #tantheta# is negative so would be #csctheta# as domain for #theta# is #[-pi/2,pi/2]#.

hence #csctheta=csc(tan^(-1)(-2))=-sqrt5/2#

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