SOLUTION: Find the exact solutions of the equation in the interval [0, 2π) (7 sin 2x + 7 cos 2x)^2 = 49

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Question 855451: Find the exact solutions of the equation in the interval [0, 2π)
(7 sin 2x + 7 cos 2x)^2 = 49
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact solutions of the equation in the interval [0, 2π)
(7 sin 2x + 7 cos 2x)^2 = 49
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Divide thru by 7 to get:
sin(2x) + cos(2x) = 7
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Note: Since neither sin nor cos can exceed one,
their sum cannot be 7.
Ans: No solution.
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: I'll get you started


( 7sin(2x) + 7cos(2x) )^2 = 49


7sin(2x) + 7cos(2x) = 7 or 7sin(2x) + 7cos(2x) = -7 ... take the square root of both sides (don't forget about the plus/minus)


sin(2x) + cos(2x) = 1 or sin(2x) + cos(2x) = -1 ... divide everything by 7