SOLUTION: What are the steps I should take to solve for x in this trigonometric equation? {{{ cos^2(x)-sin^2(x)=sin(x) }}}

Algebra ->  Trigonometry-basics -> SOLUTION: What are the steps I should take to solve for x in this trigonometric equation? {{{ cos^2(x)-sin^2(x)=sin(x) }}}      Log On


   

Question 986789: What are the steps I should take to solve for x in this trigonometric equation?
+cos%5E2%28x%29-sin%5E2%28x%29=sin%28x%29+
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
cos%5E2%28x%29%2Bsin%5E2%28x%29=1 and u=sin%28x%29 to first solve for u



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u is a variable. ANY variable other than x will work. Just pick and use a variable to help with variable management in the solution process.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
What are the steps I should take to solve for x in this trigonometric equation?
+cos%5E2%28x%29-sin%5E2%28x%29=sin%28x%29+
cos%5E2%28x%29+%2B+sin%5E2%28x%29+=+1 --------> cos%5E2%28x%29+=+1+-+sin%5E2%28x%29

1+-+sin%5E2%28x%29+-+sin%5E2%28x%29+=+sin+x -------- Substituting 1+-+sin%5E2%28x%29 for cos%5E2%28x%29

2sin%5E2%28x%29+%2B+sin+x+-+1+=+0

%282sin+x+-+1%29%28sin+x+%2B+2%29+=+0

sin+x+=+1%2F2            OR           sin+x+=+-+2 (ignore)

x+=+sin%5E%28-1%29+%281%2F2%29, and highlight_green%28system%28x+=+30%5Eo_or%2Cx+=+150%5Eo%29%29