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

  • Thread starter Curl
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In summary, The expression a / ( a2*sin(t)2 + cos(t)2 ) can be reduced to a / ((a2-1)*sin(t)2 + 1) by factoring the denominator.
  • #1
Curl
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I got this expression:

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

Is there any way to reduce it using some identity?
 
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  • #2
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 ?
 
  • #3
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).
 
  • #4
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
 
  • #5
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.
 

1. What is the purpose of reducing an expression?

Reducing an expression involves simplifying it to its simplest form. It makes the expression easier to work with and can help to reveal relationships between different variables.

2. Why is the expression being divided by the common term?

In this expression, a2 is a common term in both the numerator and denominator. Dividing by this term helps to eliminate it and simplify the expression.

3. Can this expression be further reduced?

No, this expression is already reduced to its simplest form. All common terms have been eliminated and the expression cannot be simplified any further.

4. What is the significance of the trigonometric functions in this expression?

The trigonometric functions, sin and cos, represent the relationship between sides and angles in a right triangle. In this expression, they are used to represent the relationships between different variables.

5. How is reducing an expression useful in real-world applications?

Reducing an expression can help to simplify complex equations and make them easier to solve. This can be useful in many fields, such as engineering, physics, and finance, where complex calculations are often required.

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