SOLUTION: If (sec x-2)(2sec x-1)=0

Question 80734: If (sec x-2)(2sec x-1)=0
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(sec x-2)(2sec x-1)=0
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2sec^2x-3secx +2=0
(2secx+1))(secx-2)=0
secx= -1/2 or secx = 2
Since sec has no value between -1 and 1 only secx=2 is a viable answer:
Therefore : secx=2 or cosx=1/2:
and x = 60 degrees or 300 degrees.
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Foil

Combine like terms
Let

Now factor to solve for y (note: this solver uses x instead of y):

ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'solving_by_factoring'.

Error occurred executing solver 'solving_by_factoring' .

Since we have the solutions

or

we can say

or

which is equivalent to

or

Now invert both sides

or

Now take the arccosine of both sides to solve for x

or

Since the arccosine of 2 is undefined we must discard that answer. So our answer is
where n is an integer
or
where n is an integer

which is equivalent in degrees:

where n is an integer
or
where n is an integer
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