How do you evaluate sec(tan^-1(sqrt3))sec(tan−1(√3)) without a calculator?

1 Answer
Bdub
Oct 12, 2016

sec(tan^-1(sqrt3))=sec(60^@)=1/cos(60^@) = 1/(1/2)=2sec(tan−1(√3))=sec(60∘)=1cos(60∘)=112=2

Explanation:

sec(tan^-1(sqrt3))sec(tan−1(√3))->From the special triangle 30^@-60^@-90^@30∘−60∘−90∘ we have tan 60^@=sqrt3tan60∘=√3 hence 60^@=tan^-1(sqrt3)60∘=tan−1(√3)

sec(60^@)=1/cos(60^@) = 1/(1/2)=2sec(60∘)=1cos(60∘)=112=2

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