- #1
kathyjoan
- 4
- 0
Homework Statement
sin4x/(1-cos4x) * (1-cos2x)/cos2x = tan x
HallsofIvy said:Well, gosh, there seems to be some things missing! Do you really think saying "I don't feel like making any attempt at all" is a good way to convince people to help you?
kathyjoan said:I have tried sin4x=sin(2x+2x)=2sin2xcos2x
(2sin2x/(1-cos4x))*1-cos2x
(2sin2x-2sin2xcos2x)/(1-cos4x)
2sin2x(1-cos2X)/1-cos4x
cos2x=1-2sin^2x
cos4x= cos^2 2x + sin^2 2x
can I do sin2x=sin(x+x)=sinxcosx+cosxsinx=sinx(2cosx)
I end up with 4sinxcosx=tanx? not great
The purpose of this proof is to show the equality between the left side and the right side of the equation, and to demonstrate the relationship between the trigonometric functions involved.
To solve this proof, we will use algebraic manipulation and trigonometric identities to simplify the expression on both sides of the equation until they are equal.
First, we will use the double angle identity for sine to rewrite sin4x as 2sin2xcos2x. Then, we will use the Pythagorean identity to rewrite cos2x as 1-sin2x. Next, we will distribute the 2sin2x to both terms in the numerator and simplify. Finally, we will use the quotient identity for tangent to transform the left side of the equation into tan x, which is equal to the right side.
One helpful tip is to practice using the identities in different problems to become more familiar with them. Another tip is to create a cheat sheet or flashcards to refer to when solving similar proofs.
Yes, there may be other methods to solve this proof, such as using trigonometric substitution or graphing the functions to show that they are equal. However, the method described above is a common and straightforward approach for solving this type of proof.