Asked by Bethany
How would I solve the following equation for x?
2 sin^2(x) + 3 tanx secx = 2
I've tried the problems from different approaches, but couldn't come up with a solution. Could you please provide your thought process. It would be greatly appreciated. Thanks!
2 sin^2(x) + 3 tanx secx = 2
I've tried the problems from different approaches, but couldn't come up with a solution. Could you please provide your thought process. It would be greatly appreciated. Thanks!
Answers
Answered by
MathMate
One way is to use the following identities to transform all terms to sin(x):
sec(x)=1/cos(x)
(1-cos²(x))=sin²(x)
and the resulting <i>quartic</i> equation in sin(x) can be solved. Reject roots whose absolute value exceed 1.
Double check with a plot of the function.
sec(x)=1/cos(x)
(1-cos²(x))=sin²(x)
and the resulting <i>quartic</i> equation in sin(x) can be solved. Reject roots whose absolute value exceed 1.
Double check with a plot of the function.
Answered by
MathMate
For the solution of the quartic, you should get 0.44 and 1.59 as the approximate real solutions. The latter is rejected because arcsin of 1.59 is undefined.
Thus, solve for x=asin(0.44).
Following link shows the graph:
http://img8.imageshack.us/img8/3576/1285951135.png
Thus, solve for x=asin(0.44).
Following link shows the graph:
http://img8.imageshack.us/img8/3576/1285951135.png
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