Mastering Trigonometric Equations: Solving cos 2x-cos^2 x=0

In summary, the conversation discusses how to solve the equation cos 2x-cos^2 x=0 by using the double angle identity for cosine and substituting in different identities for cos(2x). The conversation ends with a suggestion to replace cos^2 x with y and solve for y.
  • #1
lep11
380
7

Homework Statement


cos 2x-cos^2 x=0

The Attempt at a Solution


I have no idea.
 
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  • #2
Try getting everything in terms of ##cos^{2}{x}##

What is ##cos(2x)## equaled to? Hint. Double angle identity.
 
  • #3
BloodyFrozen said:
Try getting everything in terms of ##cos^{2}{x}##

What is ##cos(2x)## equaled to? Hint. Double angle identity.

cos2x=2cos^2 -1
Therefore 2cos^2 x -1 -cos^2 x=0
How to continue?
 
  • #4
lep11 said:
cos2x=2cos^2 -1
Therefore 2cos^2 x -1 -cos^2 x=0
How to continue?

Don't substitute it in yet.

##cos(2x)## has multiple identities; it also equals:

$$cos(2x) = cos^{2}(x) - sin^{2} (x)$$

How can you change the ##sin^{2} (x)## into cosines?
 
Last edited:
  • #5
Anyone?
 
  • #6
You already had 2cos^2 x -1 -cos^2 x=0.

Can you replace each occurrence of (cos^2 x) by y?
And then solve for y?
 

FAQ: Mastering Trigonometric Equations: Solving cos 2x-cos^2 x=0

What is a tricky trigonometric equation?

A tricky trigonometric equation is a mathematical equation that involves trigonometric functions, such as sine, cosine, and tangent, and may require advanced techniques to solve.

How do you solve a tricky trigonometric equation?

Solving a tricky trigonometric equation requires knowledge of trigonometric identities and techniques such as substitution, factoring, and trigonometric identities. It may also involve using a calculator or computer program.

Why are trigonometric equations considered tricky?

Trigonometric equations can be considered tricky because they often involve multiple trigonometric functions and may require creative problem-solving techniques to solve. Additionally, they may have multiple solutions or no real solutions.

Can you give an example of a tricky trigonometric equation?

One example of a tricky trigonometric equation is sin(x) + 2cos(x) = 3. This equation involves both sine and cosine functions and cannot be solved using basic algebraic techniques.

How can solving tricky trigonometric equations be useful?

Solving tricky trigonometric equations can be useful in various fields, such as engineering, physics, and astronomy, where trigonometric functions are commonly used to model and solve real-world problems. It can also improve problem-solving skills and critical thinking abilities.

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