Trigonometry help

Here is my problem
My math account tells me the answer is  
I would assume that to remove the 2 in the denominator both sides were multiplied by 2. What I don't understand is how the square root was removed. if you square both sides the 2's should become 4's correct? That,s the part of my confusion can some one please explain whats going and tell me what math principle I am missing here or just not applying correctly.
Leo TorresSQL DeveloperAsked:
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I think the 2 should be sqrt(2):
sqrt(2)   sqrt(2)       2            1
------- * ------- = ----------- = --------
   2      sqrt(2)   2 * sqrt(2)    sqrt(2)

tan(x)^2 = (sqrt(2)/2) * sec(x)
tan(x)^2 = 1/sqrt(2) sec(x)
sqrt(2) * tan(x)^2 = sec(x)
sec(x) = sqrt(2) * tan(x)^2

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Also, fyi -*+sec%28x%29
When I put the same equation into, it came up with an answer of:
sec(x) = tan(x)

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ozoCommented: seems to be giving you incorrect answers.
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Leo TorresSQL DeveloperAuthor Commented:
I will try again.. I used the one on my phone
>> I will try again.. I used the one on my phone
I used on my laptop and it gave me the above incorrect answer. Right now, I would not put my trust in, unless there is a input notation that is different than what I wrote.
If your goal is to solve the equation for x, rather than to get to work, then you may be able to find solutions to tan(x)*sqrt(2) = csc(x) inspection.
Leo TorresSQL DeveloperAuthor Commented:
Dont need to solve I could always use the apps to give me answers I wanted to know the logic used to simplify. But something about that answer troubles me. I will try another app when I get home.
You can plot both sides in Excel from 0 to pj and see if they match.
What troubles you about what answer?

Can you solve it in this form?
1-cos^2(x) = cos(x)/sqrt(2)
Leo TorresSQL DeveloperAuthor Commented:
I don't understand what rule was used for the final simplification. How was the sqrt moved out and the tan stayed squared.  And it didnt become 4th power.
The only simplifications I see without a sqrt come come and are incorrect.
Perhaps they printed a square root in a font that we don't have.
Leo TorresSQL DeveloperAuthor Commented:
Interesting i didn't by that solution but i would think the program works correctly so thats why i would like to know what operation was preformed to get final solution. The only operation i was able to preform is multiply both sides by 2. Moving the sqrt to me has remained the mystery
If you are referring to,
it is not a correct transform of,
as others have noted, it is missing a sqrt

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Leo TorresSQL DeveloperAuthor Commented:
I used derive to simplify and i got this view
Not quite what I thought but I least I see whats going on here.
Leo TorresSQL DeveloperAuthor Commented:
Thank you guys
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