- #1
Aaron H.
- 13
- 0
Homework Statement
Prove the identity.
Homework Equations
http://postimage.org/image/vjhwki1ax/
The Attempt at a Solution
http://s13.postimage.org/jkhubi4lz/DSC03534.jpg
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Villyer said:I noticed that after all of your work, you got the problem to cos(3x)cos(x)-sin(x)sin(3x).
Villyer said:Using sec(x) = 1/cos(x) and csc(x) = 1/sin(x);
cos(3x)/sec(x) - sin(x)/csc(3x)
cos(3x)/(1/cos(x)) - sin(x)/(1/sin(3x))
cos(3x)cos(x) - six(x)sin(3x)
Looking at the OP's solution, the OP went the complicated route to go from the LHS to the bolded part above. Villyer just simplified the process.Curious3141 said:I can't view his solution.
Aaron H. said:cos(3x)cos(x) - six(x)sin(3x)
cos (4x)
cos^2 2x - sin^2 2x
Thanks all.
To prove a trigonometric identity, you need to use the basic trigonometric identities, algebraic manipulation, and sometimes the unit circle. It is important to start with one side of the equation and manipulate it until it matches the other side. This step-by-step guide will walk you through the process.
The basic trigonometric identities are sine, cosine, and tangent. They are defined as:
Algebraic manipulation involves using algebraic properties and rules to simplify and transform an equation. Some common techniques include using the distributive property, combining like terms, and factoring.
The unit circle is a circle with a radius of 1 that is centered at the origin of a coordinate plane. It is used to relate the values of sine, cosine, and tangent to the coordinates on the circle. To use the unit circle to prove a trigonometric identity, you may need to convert trigonometric functions into their corresponding coordinates on the unit circle.
Proving a trigonometric identity helps to establish the relationship between different trigonometric functions and to show that they are equivalent. It also allows for the simplification of complex trigonometric expressions and can be useful in solving trigonometric equations and problems.