Why Can't I Simplify This Trigonometric Equation?

In summary, the given equation can be simplified to sec x tan x by using the identities csc x = 1/sin x and sec x = 1/cos x. To solve the equation, one side must be manipulated to match the other side, and by multiplying both the numerator and denominator by sin x, the left side can be simplified to match the right side.
  • #1
Adam2987
49
0

Homework Statement



1/cscx-sinx = secx tanx

Homework Equations



cscx = 1/sinx
secx = 1/cosx

The Attempt at a Solution



1/cscx-sinx = secx tanx

L.S.
= 1/cscx-sinx
= 1/(1/sinx)-sinx

R.S.
= secx tanx
= (1/cosx)(sinx/cosx)

This is where I'm getting confused. Why can't I make the L.S equal the Right side?
 
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  • #2
Adam2987 said:

The Attempt at a Solution



1/cscx-sinx = secx tanx

L.S.
= 1/cscx-sinx
= 1/(1/sinx)-sinx

R.S.
= secx tanx
= (1/cosx)(sinx/cosx)

This is where I'm getting confused. Why can't I make the L.S equal the Right side?

Start with one side alone and make that match the other side.


Adam2987 said:

The Attempt at a Solution



1/cscx-sinx = secx tanx

L.S.
= 1/cscx-sinx
= 1/(1/sinx)-sinx

What happens if you multiply both the numerator and denominator by sinx/sinx ?
 
  • #3
(1/sinx)(sinx/sinx) = sin^2x - sinx?
 
  • #4
Adam2987 said:
(1/sinx)(sinx/sinx) = sin^2x - sinx?

[tex]\frac{1}{\frac{1}{sinx}-sinx} \times \frac{sinx}{sinx}[/tex]

Redo it.
 
  • #5
Hmmm. Do I multiply everything in the first denominator by sinx? Or just the - sinx?

I get sinx/sinx-sin2x. I think... I've never seen mulitiplication like this. It's probably something easy, I've just never done it yet.
 
  • #6
Adam2987 said:
Hmmm. Do I multiply everything in the first denominator by sinx? Or just the - sinx?

I get sinx/sinx-sin2x. I think... I've never seen mulitiplication like this. It's probably something easy, I've just never done it yet.

Multiply everything in the numerator by sinx, and multiply everything in the denominator by sinx.
 
  • #7
ok so I get sinx/(sinx/sin^2x)-sin^2x

If I divide that I end up with sinx-sinx = 0?
 
  • #8
err or would it be sinx/sinx-sinx?
 
  • #9
rock.freak667 said:
[tex]\frac{1}{\frac{1}{sinx}-sinx} \times \frac{sinx}{sinx}[/tex]

If that's the actual problem(can't tell from your original post), then:

get a common denominator:

1/((1-((sin x)^2))/ sin x) becomes:

(sin x)/(1-((sin x)^2)) --> 1 - sin^2 x = cos^2 x:

(sin x)/((cos x)^2) = sec x tan x
 

Related to Why Can't I Simplify This Trigonometric Equation?

1. What are trigonometric identities?

Trigonometric identities are mathematical equations that involve trigonometric functions (such as sine, cosine, tangent) and are true for all values of the variables involved.

2. Why is it important to learn how to solve trig identities?

Solving trig identities is important because they are used in many applications, such as physics, engineering, and navigation. They also serve as the basis for more complex trigonometric equations and can help simplify calculations.

3. What are some common strategies for solving trig identities?

Some common strategies for solving trig identities include using basic trigonometric identities (such as Pythagorean identities), manipulating the equations using algebraic techniques, and converting trigonometric functions to their equivalent forms.

4. How can I check if my solution for a trig identity is correct?

You can check if your solution for a trig identity is correct by substituting the values of the variables into the equation and simplifying both sides. If the resulting equations are equal, then your solution is correct.

5. Are there any tips for memorizing trigonometric identities?

Some tips for memorizing trigonometric identities include practicing regularly, understanding the relationships between different identities, and creating memory aids such as flashcards or mnemonic devices.

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