"using the "color(blue)"trigonometric identities"using the trigonometric identities
•color(white)(x)tan^2x+1=sec^2x∙xtan2x+1=sec2x
rArrsecx=+-sqrt(tan^2x+1)⇒secx=±√tan2x+1
•color(white)(x)sin^2x+cos^2x=1∙xsin2x+cos2x=1
rArrsinx=+-sqrt(1-cos^2x)⇒sinx=±√1−cos2x
"Given "tanx<0" and "cosx>0" then"Given tanx<0 and cosx>0 then
"x is in the fourth quadrant"x is in the fourth quadrant
tanx=-7/24rArrcotx=1/tanx=-24/7tanx=−724⇒cotx=1tanx=−247
secx=+sqrt((-7/24)^2+1)secx=+√(−724)2+1
color(white)(secx)=sqrt(49/576+1)=sqrt(625/576)=25/24secx=√49576+1=√625576=2524
rArrcosx=1/secx=24/25⇒cosx=1secx=2425
rArrsinx=-sqrt(1-(24/25)^2)⇒sinx=−√1−(2425)2
color(white)(rArrsinx)=-sqrt(1-576/625)=-sqrt(49/625)=-7/25⇒sinx=−√1−576625=−√49625=−725
rArrcscx=1/sinx=-25/7⇒cscx=1sinx=−257
