Question

Solve sec2theta + tantheta - 3 =0 for 0

Answer 1

Answer:

Ф = $\frac{\pi }{4} ,\frac{5\pi}{4}$

Step-by-step 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 $\frac{\pi}{4}$ and $\frac{5\pi}{4}$ so these are the solutions to the problem