keep getting wrong answer

[cotfw]

I'm supposed to solve for x:

tanX + 2cosX = secX

I started by moving 2cosX to the other side, then squaring both sides:

tan²X = sec²X - 4 + 4 cos²X

Then I turned tan²X into sec²X - 1 and cancelled out the two sec²X's:

-1 = -4 + 4cos²X

Which turned into 3/4 = cos²X

And then cosX = +-(√3)/2

From here I figured X would be π/6 + 2πn, 5π/6 + 2πn, 7π/6 + 2πn, 11π/6 + 2πn, but my book's answer only has the last two of these, which doesn't make any sense to me.

 

[Deleted member 4993]

I'm supposed to solve for x:

tanX + 2cosX = secX

I started by moving 2cosX to the other side, then squaring both sides:

tan²X = sec²X - 4 + 4 cos²X

Then I turned tan²X into sec²X - 1 and cancelled out the two sec²X's:

-1 = -4 + 4cos²X

Which turned into 3/4 = cos²X

And then cosX = +-(√3)/2

From here I figured X would be π/6 + 2πn, 5π/6 + 2πn, 7π/6 + 2πn, 11π/6 + 2πn, but my book's answer only has the last two of these, which doesn't make any sense to me.

Since you used "square" operation, extraneous answers have crept in. So you need to find, out of the four solutions, which do satisfy the given (original) equation.

 

[cotfw]

Yep that was the issue. Thanks