91Ó°ÊÓ

What is the reciprocal property for sec \(x ?\)

Write \(\tan x\) in terms of \(\sin x\) and \(\cos x\)

By appropriate operations on the Pythagorean property \(\cos ^{2} x+\sin ^{2} x=1,\) derive the Pythagorean property \(\cot ^{2} x+1=\csc ^{2} x\)

Calculate the exact value of the inverse function geometrically. Assume the principal branch in all cases. Check your answers by direct calculation. $$\tan \left(\cot ^{-1} 4\right)(\text { Surprise? })$$

Prove that the equation \(\tan ^{2} x-\sec ^{2} x=1\) is not an identity.