Question

I just took a math test, but there was a rigged question.
Do not worry everyone, I'm not cheating, I already took the test and asking the question after taking it. It is about trigonometry and I was getting headache attempting the problem.

Answer 1

\[\tan(3x) + 1 = \sec(3x) \]

Answer 2

Find all solutions.

Answer 3

Rigged? :) lol

Answer 4

I knew that I had to substitute the 3x with just a single x, but I just couldn't solve from there.

Answer 5

Here is my approach,
square both sides,\[\large\rm \tan^2(3x)+2\tan(3x)+1=\sec^2(3x)\]Use your Pythagorean Identity on the right side of the equation,\[\large\rm \tan^2(3x)+2\tan(3x)+1=\tan^2(3x)+1\]And then you have a lot of nice cancellations from there :)

Any confusion?

Answer 6

Wait, where did you get the 2tan(3x)
And now that you say pythagorean identity, I feel so dumb that I didn't recognize it :(

Answer 7

I'm a failure at math! Nooooooo, my test score is ruined :(

Answer 8

\[\large\rm (a+1)^2=a^2+\color{orangered}{2a}+1^2\]

Answer 9

\[\large\rm (\tan3x+1)^2=\tan^2(3x)+\color{orangered}{2\tan3x}+1^2\]

Answer 10

tan + 1 = sec

sin/cos + cos/cos = 1/cos

sin + cos = 1 (cos ≠ 0)

Answer 11

ohhhh, I understand now.

Answer 12

ya sines and cosines is another good approach :)

Answer 13

Alright, thanks guys.