Question

How do you simplify `(\sec \theta + \tan \theta ) ^ { 2}`?

Answer 1

`f(t) = (sec t + tan t)^2 = sec^2 t + tan^2 t + 2tan t.sec t` (1)
Note.
`sec^2 t = 1 + tan^2 t`
`2sec t.tan t = 2(1/cos t)(cos t/sin t) = 2/(sin t) = 2csc t`
Equation (1) becomes;
`f(t) = 2tan^2 t + 2csc t + 1`