Answer:
see the procedure
Step-by-step explanation:
we have
[tex]8cot^{2}(y)(sec^{2}(y)-1)=8[/tex]
Remember that
[tex]tan(y)=\frac{sin(y)}{cos(y)}[/tex]
[tex]tan(y)=\frac{1}{cot(y)}[/tex]
[tex]sec(y)=\frac{1}{cos(y)}[/tex]
[tex]sin^2(y)+cos^2(y)=1[/tex] -----> [tex]sin^2(y)=1-cos^2(y)[/tex]
[tex](sec^{2}(y)-1)=\frac{1}{cos^2(y)}-1=\frac{1-cos^2(y)}{cos^2(y)}=\frac{sin^2(y)}{cos^2(y)}=tan^2(y)=\frac{1}{cot^2(y)}[/tex]
substitute
[tex]8cot^{2}(y)(\frac{1}{cot^2(y)})=8[/tex]
Simplify
[tex]8=8[/tex] ----> is verified
