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TheRedDevil18
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Homework Statement
tanx-1 = cos2x
The Attempt at a Solution
I know tanx = sinx/cosx but I don't know which identity to pick for cos2x
TheRedDevil18 said:Homework Statement
tanx-1 = cos2x
The Attempt at a Solution
I know tanx = sinx/cosx but I don't know which identity to pick for cos2x
BrettJimison said:Good day TheRedDevil18
If you replace cos(2x) with 2cos2(x) - 1 ,
that will get rid of the (-1) on the left side. Then go from there...
?TheRedDevil18 said:sinx/cosx = 2cos^2(x)
sinx/cosx = 2(1-sin^2(x))
sinx/2cosx + sin^2(x) = 1
sinx/2cosx * 1/sin^2(x) = 1
No.TheRedDevil18 said:2SinxCosx = 1
sin2x = 1
x = 45
All good?
Mark44 said:If you check your work, you'll see that 45° is not a solution.
Thanks! He didn't show the original equation in his later work, and I misremembered cos2x as cos2x in my check.Pranav-Arora said:45° satisfies the given equation but RedDevil reached it with a wrong method as you pointed out.
Go back to ##tan(x) = 2 \; cos^2(x)## and write ##cos^2## as ##1/sec^2 = 1/(1+tan^2)## to get a cubic in tan(x). One solution is obvious, the other two are complex.verty said:I can't see how to solve this in an easy way. I get to
##sin(x) = 2 \; cos^3(x)##
and am stuck. I suspect something is wrong with this question.
verty said:I can't see how to solve this in an easy way. I get to
##sin(x) = 2 \; cos^3(x)##
and am stuck. I suspect something is wrong with this question.
To solve a trigonometric equation, you need to use algebraic techniques and trigonometric identities to isolate the variable (usually represented by x) on one side of the equation and the numerical value on the other side. Once the variable is isolated, you can use a calculator to find the values of the variable that satisfy the equation.
The main difference between a trigonometric equation and a regular algebraic equation is that a trigonometric equation involves trigonometric functions (such as sine, cosine, tangent) while a regular algebraic equation only involves basic arithmetic operations (such as addition, subtraction, multiplication, division).
The steps to solve a trigonometric equation using the double angle formula are as follows:1. Rewrite the trigonometric function in terms of cosine or sine using the double angle formula.2. Simplify the equation using algebraic techniques.3. Use a calculator to find the values of the variable that satisfy the equation.
Yes, there can be multiple solutions to a trigonometric equation. This is because trigonometric functions are periodic, meaning they repeat their values after a certain interval. Therefore, an equation involving trigonometric functions may have multiple solutions within the given interval.
To check if your solution to a trigonometric equation is correct, you can substitute the value of the variable into the original equation and see if it satisfies the equation. You can also graph the equation and see if the coordinates of the point of intersection match your solution.