Question

find all solutions of the trigonometric equation
2cos(x) + tan(x) = sec(x)

Answer 1

So first thing you want to do is simplify everything into sine and cosine:
2cos(x) + sin(x)/cos(x) = 1/cos(x)
Then simplify down:
2cos^2(x) + sin(x) = 1
A trigonometric identity states that 2cos^2(x) = 1 - sin^2(x) so:
1 - sin^2(x) + sin(x) = 1
-sin^2(x) + sin(x) = 0
Then you can substitute all terms sin(x) as a letter and solve as a quadratic.
-u^2 + u = 0
And solve the quadratic to get solutions (0, 1)

Answer 2

Oh, thanks!

Answer 3

Then do I plug the solutions back into the original equation?

Answer 4

Yeah to test it.

Answer 5

But I might be wrong if I messed up an identity or something

Answer 6

Hold on I'll check it

Answer 7

Okay

Answer 8

Yeah I did something wrong. Sorry I don't really remember trig identities that well

Answer 9

Do you have a sheet with them on it?

Answer 10

The identities?

Answer 11

Cos^2(x) + sin^2(x) = 1

Answer 12

1+tan^2(x)=sec^2(x)
1+cot^2(x)=csc^2(x)

Answer 13

Sorry man I can't figure this one out

Answer 14

It's good thanks anyways