Reduce Expression: a/(a2*sin2(t)+cos2(t))

  • Context: Undergrad 
  • Thread starter Thread starter Curl
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the expression a / (a²*sin²(t) + cos²(t)) and explores potential methods for reducing or simplifying it using trigonometric identities. The scope includes mathematical reasoning and exploratory approaches to algebraic manipulation.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • Some participants inquire about the possibility of reducing the expression using trigonometric identities.
  • One participant questions the relevance of the identity sin²(t) + cos²(t) in the context of the given expression.
  • Another participant emphasizes that the expression involves (a*sin(t))² + cos²(t) rather than sin²(t) + cos²(t).
  • There is a suggestion to factor the denominator to express it as (sin²(t) + cos²(t)) multiplied by another term, although the utility of this approach is uncertain.
  • One participant reports successfully factoring the expression to a / ((a² - 1)*sin²(t) + 1), but expresses uncertainty about its usefulness.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to simplify the expression, and multiple viewpoints regarding the relevance of certain identities and factoring methods remain present.

Contextual Notes

The discussion includes unresolved mathematical steps and assumptions regarding the applicability of trigonometric identities to the expression.

Curl
Messages
756
Reaction score
0
I got this expression:

a / ( a2*sin(t)2 + cos(t)2 )

Is there any way to reduce it using some identity?
 
Last edited:
Mathematics news on Phys.org
Curl said:
I got this expression:

a / ( a2*sin(t)2 + cos(t)2 )

Is there any way to reduce it using some identity?

What is sin(t)2 + cos(t)2 ?
 
sjb-2812 said:
What is sin(t)2 + cos(t)2 ?

Does that really matter, though? We're not dealing with sin^2(t)+cos^2(t). We're dealing with (a sin(t))^2 + cos^2(t).
 
Char. Limit said:
Does that really matter, though? We're not dealing with sin^2(t)+cos^2(t). We're dealing with (a sin(t))^2 + cos^2(t).

True, just trying a few things. Can we factor the bottom to give (sin2t + cos2t) x something? Might be useful, might not
 
sjb-2812 said:
True, just trying a few things. Can we factor the bottom to give (sin2t + cos2t) x something? Might be useful, might not

Well, I don't know if it helps, but I managed to factor it to this:

[tex]\frac{a}{\left(a^2-1\right)sin^2(t) + 1}[/tex]

That's the best I can do though.
 

Similar threads

High School Trigonometric Identity involving sin()+cos()
  • · Replies 11 ·
Replies
11
Views
2K
MHB Find Coefficient of Friction for Toy Car Rolling Down Slope
  • · Replies 6 ·
Replies
6
Views
2K
MHB Prove (tan^2 t−1)/(sec^2 t)=(tan t−cot t)/(tan t+cot t)
  • · Replies 3 ·
Replies
3
Views
2K
How to Simplify This Trigonometric Equation Using Substitutions?
  • · Replies 4 ·
Replies
4
Views
1K
New axis of rotation for composite of rotations in Euclidean space
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Pair of interacting systems, driven coupled harmonic oscillators
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Trig Manipulations I'm Not Getting
  • · Replies 1 ·
Replies
1
Views
2K
MHB 7.t.27 write eq for a sinusiol graph
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How to Find the Area of a Triangle Using Basic Trigonometry?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Solving simultaneous vector equations
  • · Replies 11 ·
Replies
11
Views
3K