Question

what is tan theta written in terms of sec theta

Answer 1

Draw a right triangle sides a and b and hypotenuse h.
Let theta be angle opposite side b.

tan theta = b/a

sec theta = 1/cosine theta

cosine theta = a/h

h^2 = a^2 + b^2

Messy, but do able.

sec theta = 1/ cosine theta
and you are done.

Answer 2

Thank you

Answer 3

The other possible approach is that
tan@ = sin@/cos@ =sin@ sec@.
Depends on what the question is getting at. You aer welcome.

Answer 4

Pythagorean Identity: sin^2(t) + cos^2(t) = 1
Divide both sides by cos(t):
tan^2(t) + 1 = sec^2(t)
Solve for tan(t):
tan(t) = +- sqrt( sec^2(t) - 1 )