Proving Sin 6x Cos 4x + Cos 4x sin 2x = Cos 2x tan 8x

  • Context: Undergrad 
  • Thread starter Thread starter texas_kiwi
  • Start date Start date
  • Tags Tags
    Cos Sin Tan
Click For Summary
SUMMARY

The equation Sin 6x Cos 4x + Cos 4x sin 2x = Cos 2x tan 8x can be proven using trigonometric identities. The expression Sin 6x Cos 4x simplifies to 1/2(Sin 10x + Sin 2x), while Cos 4x sin 2x simplifies to 1/2(Sin 6x - Sin 2x). Combining these results leads to the expression 1/2(Sin 10x + Sin 6x), which can be further manipulated to show the relationship with Cos 2x tan 8x. The discussion also touches on a personal discovery regarding the addition and subtraction of tangent functions.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with the sine and cosine functions
  • Knowledge of tangent function properties
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the derivation of trigonometric identities
  • Learn about the sine addition formulas
  • Explore the properties of the tangent function
  • Investigate advanced trigonometric equations and their proofs
USEFUL FOR

Students and educators in mathematics, particularly those focusing on trigonometry, as well as anyone interested in proving complex trigonometric identities.

texas_kiwi
Messages
2
Reaction score
0
I am trying to prove this equation:

Sin 6x Cos 4x + Cos 4x sin 2x =
Cos 2x tan 8x​
Tan 8x​
does anyone have any idea??
 
Physics news on Phys.org
[tex]\sin 6x\cos 4x = \frac{1}{2}(\sin 10x + \sin 2x)[/tex]
[tex]\cos 4x\sin 2x = \frac{1}{2}(\sin 6x - \sin 2x)[/tex].

So we get [tex]\frac{1}{2}(\sin 10x + \sin 6x)[/tex]

or [tex]\sin 8x\cos 2x[/tex].

The second expression is not right. Just plug in some values.
 
Last edited:
yes I will tray to slove it

before some month I one like this and I see new law
tan(a)+tan(b)
tab(a)-tan(b)

I discoverd new law juist in my opinion
 

Similar threads

Undergrad Prove that the derivative of tan(2x) - cot(2x) equals....
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Integrating a Complex Integral using Substitution and Simplification
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Having trouble understanding a seemingly simple u-substitution
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Did Math DF's integral calculator make a glaring mistake?
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Landscape Fabric Roll
  • · Replies 8 ·
Replies
8
Views
3K
MHB Integrating $-3x\cos{4x}$: Step-by-Step
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad How Do You Integrate ##\int \tan 2x \ dx##?
  • · Replies 3 ·
Replies
3
Views
17K
Solving a trigonometric equation with multiples of ##\tan##
  • · Replies 7 ·
Replies
7
Views
3K
Solve the equation: ##\tan x ⋅\tan 4x = 1##
  • · Replies 4 ·
Replies
4
Views
2K
MHB Find $\tan(2x)$ Given $\cos(x-y)$ and $\sin(x+y)$
  • · Replies 3 ·
Replies
3
Views
2K