SOLUTION: find x for {{{tan((x/2)-(pi/2))=sqrt(2)}}} I got {{{x=2arccot(-sqrt(2)) + 2*pi*n}}}where n is all integers, but it's wrong? i changed tan to -cot so it would be cot(x/2)= -sq

Algebra ->  Trigonometry-basics -> SOLUTION: find x for {{{tan((x/2)-(pi/2))=sqrt(2)}}} I got {{{x=2arccot(-sqrt(2)) + 2*pi*n}}}where n is all integers, but it's wrong? i changed tan to -cot so it would be cot(x/2)= -sq      Log On


   

Question 1132674: find x for tan%28%28x%2F2%29-%28pi%2F2%29%29=sqrt%282%29
I got x=2arccot%28-sqrt%282%29%29+%2B+2%2Api%2Anwhere n is all integers, but it's wrong?
i changed tan to -cot so it would be cot(x/2)= -sqrt2 and then solved x for that.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
x = 2(pi*n -cot^(-1) (sqrt(2)), where n is an element of Z
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Here how to get this answer
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-cot(x/2) = sqrt(2)
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Multiply both sides by -1 to simplify the equation.
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cot(x/2) = -sqrt(2)
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Eliminate the cotangent from the left hand side
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Take the inverse cotangent of both sides
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x/2 = pi * n -cot^(-1)(sqrt(2)) for n an element of Z
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Solve for x
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x = 2 * pi * n -2 * cot^(-1)(sqrt(2)) for n an element of Z
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x = 2 * (pi * n -cot^(-1)(sqrt(2)) for n an element of Z