(sinθ/(1-cotθ)) + (cosθ/(1-tanθ)) = cosθ + sinθ

  • Thread starter PsychoMessiah
  • Start date
In summary, the equation (sinθ/(1-cotθ)) + (cosθ/(1-tanθ)) = cosθ + sinθ represents an identity in trigonometry that holds true for all values of θ. It can be derived using basic trigonometric identities and is significant in simplifying and solving trigonometric expressions and equations. It can also be used in practical applications, without any restrictions on the values of θ.
  • #1
PsychoMessiah
5
0

Homework Statement


I have to prove that:

(sinθ/(1-cotθ)) + (cosθ/(1-tanθ)) = cosθ + sinθ


Homework Equations





The Attempt at a Solution


Here's my attempt at solution...
6gy26c.jpg

 
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  • #2
Very close!
a2 - b2 = ?
 
  • #3
OMG how unbelievably stupid of me...
obviously (a - b)(a + b)

thanks a lot bro... :D
 
  • #4
th4450,
If you post a photo of your work in another thread,
1) Take a better picture. This one was so dark it was barely legible.
2) Shrink the image so that it is no larger than 800 x 600 pixels.
 

FAQ: (sinθ/(1-cotθ)) + (cosθ/(1-tanθ)) = cosθ + sinθ

What does the equation (sinθ/(1-cotθ)) + (cosθ/(1-tanθ)) = cosθ + sinθ represent?

This equation represents an identity in trigonometry, where the left side is equal to the right side for all values of θ.

How is this equation derived?

This equation can be derived using basic trigonometric identities, such as sinθ = 1/cscθ and cosθ = 1/secθ.

What is the significance of this equation in mathematics?

This equation is significant because it helps in simplifying and solving various trigonometric expressions and equations.

Can this equation be used for practical applications?

Yes, this equation can be used in practical applications, such as solving real-life problems involving triangles and angles.

Are there any restrictions on the values of θ for this equation to hold true?

No, there are no restrictions on the values of θ for this equation to hold true. It is valid for all values of θ.

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