Question

Solve sec2theta + tantheta - 3 =0 for 0

Answer 1

Ф =
`(\pi )/(4) ,(5\pi)/(4)`

Explanation:

It is a bit difficult to input the work here, so I uploaded an image

• First we can use the trig identities to change sec²(Ф) to tan²(Ф) + 1
• Then we can combine like terms
• Then we can factor this as a polynomial function
• Then we can set each term equal to zero and solve for Ф
• The first term tan(Ф) - 2 = 0 has no solution because tan(Ф) ≠ -2 anywhere
• The second term tan(Ф) - 1 = 0 has two solutions of
  `(\pi)/(4)` and
  `(5\pi)/(4)` so these are the solutions to the problem