A dog wants to catch a cat. The dog follows the path whose equation is `y-x=0` while the cat follows the path whose equation is `x^(2)+y^(2)=8`. The coordinates of possible points of catching the cat are:

Explanation

(i) `sin 30^(@)+cos 60^(@)=1/2+1/2=1" "` (ii) `sin 0^(@)-cos 0^(@)=0-1=-1`
(iii) `tan 45^(@)-tan 37^(@)=1-3/4=1/4" "` (iv) `sin 390^(@)=sin (360^(@)+30^(@))=sin 30^(@)=1/2`
(v) `sin 150^(@)= sin (90^(@)+60^(@))=cos 45^(@)=1/sqrt(2)" "` (vi) `tan 420^(@)=tan (360^(@)+60^(@))= tan 60^(@)=sqrt(3)`
(vii) `sin 150^(@)= sin (90^(@)+60^(@))=cos 60^(@)=1/2` or `sin 150^(@)= sin (180^(@)-30^(@))= sin 30^(@)=1/2`
(viii) `cos 120^(@)= cos (180^(@)-60^(@))=- cos 60^(@)=-1/2" "` (ix) `tan 135^(@)=tan (180^(@)-45^(@))=-tan 45^(@)=-1`
(x) `sin 330^(@)= sin (360^(@)-30^(@))=- sin 30^(@)=-1/2" "` (xi) `cos 300^(@)=cos (360^(@)-60^(@))= cos 60^(@)=1/2`
(xii) `sin (-30^(@))=-sin 30^(@)-=1/2 " "` (xiii) `cos (-60^(@))=+ cos 60^(@)=1/2`
(xiv) `tan (-45^(@))=-tan 45^(@)=-1`
(xv) `sin (-150^(@))=-sin (150^(@))=- sin (180^(@)-30^(@))=- sin 30^(@)=-1/2`