- #1
kasse
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Which trigonometric identitiy are used to transform 2(cos(x))^2+2cos(x)sin(x) into 0?
Transforming Trigonometric Identities: Solving 2(cosx)^2+2cosxsinx=0
- Thread starter kasse
- Start date
In summary, transforming trigonometric identities simplifies complex expressions and equations, making them easier to solve. To solve equations like 2(cosx)^2+2cosxsinx=0, one must use trigonometric identities to simplify the expression. Common identities include Pythagorean, double angle, and half angle identities. It is important to check for extraneous solutions when solving trigonometric equations. Tips for solving equations involving trigonometric identities include simplifying the expression and being familiar with common identities.
- #2
Curious3141
Homework Helper
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If you want to show that [tex]2\cos^2 x + 2\cos x \sin x = 0[/tex] identically, you can't because it isn't true.
If you want to solve the equation [tex]2\cos^2 x + 2\cos x \sin x = 0[/tex] that's a different matter entirely. So what is it you want to do?
If you want to solve the equation [tex]2\cos^2 x + 2\cos x \sin x = 0[/tex] that's a different matter entirely. So what is it you want to do?
- #3
kasse
- 384
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Sorry, I gave you the wrong eq. Solved in on my own here.
What's up in Singapore?
What's up in Singapore?
- #4
Curious3141
Homework Helper
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kasse said:
Mostly the sky, I guess.
Related to Transforming Trigonometric Identities: Solving 2(cosx)^2+2cosxsinx=0
What is the purpose of transforming trigonometric identities?
Transforming trigonometric identities helps simplify complex trigonometric expressions and equations, making them easier to solve. This is especially useful when working with trigonometric equations in calculus and other higher level math courses.
How do I solve an equation like 2(cosx)^2+2cosxsinx=0?
To solve this equation, you need to use trigonometric identities to simplify the expression. In this case, you can use the double angle identity for cosine (cos2x = 1 - 2sin^2x) to rewrite the equation as 2(1-2sin^2x)+2sinx=0. Then, you can use the quadratic formula to solve for sinx, and then use inverse trigonometric functions to find the solutions for x.
What are some common trigonometric identities used in transforming equations?
Some common trigonometric identities used in transforming equations include the Pythagorean identities (sin^2x + cos^2x = 1, tan^2x + 1 = sec^2x, cot^2x + 1 = csc^2x), the double angle identities (sin2x = 2sinxcosx, cos2x = cos^2x - sin^2x), and the half angle identities (sin(x/2) = ±√[(1-cosx)/2], cos(x/2) = ±√[(1+cosx)/2]).
Why is it important to check for extraneous solutions when solving trigonometric equations?
Trigonometric equations often have multiple solutions, and sometimes the process of transforming the equation can introduce extraneous solutions, which are solutions that do not satisfy the original equation. Checking for extraneous solutions helps ensure that you have found all the correct solutions to the equation.
Are there any tips for solving equations involving trigonometric identities?
One tip for solving equations involving trigonometric identities is to try to simplify the expression as much as possible before attempting to solve. This can involve using identities, factoring, or manipulating the equation in other ways. Additionally, it is important to be familiar with common trigonometric identities and how to apply them in different situations.
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