Question

What is the exact value of the expression: sec2 80° − tan2 80°?

Answer 1

`sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(80^o)-tan^2(80^o)\implies \cfrac{1}{cos^2(80^o)}-\cfrac{sin^2(80^o)}{cos^2(80^o)} \\\\\\ \cfrac{1-sin^2(80^o)}{\underset{\textit{using this LCD}}{cos^2(80^o)}}\implies \cfrac{cos^2(80^o)}{cos^2(80^o)}\implies 1`