SOLUTION: Given the equation: cos(x)1/sec(x)=-sqrt2 Solve for x: State which trigonometric identity/ies will give a result of -sqrt2. Please include a solution too, thank you so much.

Algebra ->  Trigonometry-basics -> SOLUTION: Given the equation: cos(x)1/sec(x)=-sqrt2 Solve for x: State which trigonometric identity/ies will give a result of -sqrt2. Please include a solution too, thank you so much.      Log On


   

Question 1173762: Given the equation:
cos(x)1/sec(x)=-sqrt2
Solve for x: State which trigonometric identity/ies will give a result of -sqrt2. Please include a solution too, thank you so much.
Answer by ikleyn(52905) About Me  (Show Source):
You can put this solution on YOUR website!
.

As everybody knows,  sec(x) = 1%2Fcos%28x%29.


THEREFORE the left side of your equation is


    cos%28x%29%2A%281%2Fsec%28x%29%29 = cos%28x%29%2Fsec%28x%29 = cos%28x%29%2F%28%281%2Fcos%28x%29%29%29 = cos%5E2%28x%29.



The right side of the equation is  - sqrt%282%29.


The left side is always positive as the square of a real number.


The right side is a negative real number.



THEREFORE, the given equation HAS NO solutions.     ANSWER


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