Verify trigonometric identity

Please do not post the same question in multiple threads. In summary, the conversation is about verifying the identity 1+sec(-∅)/sin(-∅+tan(-∅) = -csc ∅ and one user suggests multiplying both sides by sin∅ + tan∅. Another user asks for clarification and another suggests rewriting the trigonometric functions in terms of sine and cosine.
  • #1
louie3006
54
0

Homework Statement



verify the identity :
1+sec(-∅)/sin(-∅+tan(-∅) = -csc ∅

Homework Equations





The Attempt at a Solution


1+sec∅/-sin-tan∅ = -csc∅

I don't know where to start from, does anyone have any idea?
 
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  • #2
louie3006 said:
1+sec∅/-sin-tan∅ = -csc∅

I don't know where to start from, does anyone have any idea?

Hi louie3006!

Just do the obvious … multiply both sides by sin∅ + tan∅ :smile:
 
  • #3
do you mean conjugate the left side of the equation ?
 
  • #4
are those minus signs before ∅?
i agree with tiny-tim, multiply both side by (sin∅ + tan∅) and you should see it.
if it helps, you can rewrite sec, csc and tan in terms of sin and cos.
 
  • #5
I need to verify the identity of this problem

tan^2(x/2)=(sec x-1)/(sec x+1)
 
  • #6
You have already started a new thread for this problem, which is the right thing to do.
 

1. What is a trigonometric identity?

A trigonometric identity is an equation that is true for all values of the variables involved. It can also be thought of as a relationship between different trigonometric functions.

2. Why is it important to verify trigonometric identities?

Verifying trigonometric identities is important because it allows us to manipulate and simplify trigonometric expressions, making them easier to work with. It also helps us to understand the relationships between different trigonometric functions.

3. How do you verify a trigonometric identity?

To verify a trigonometric identity, we use algebraic manipulations and trigonometric identities (such as the Pythagorean identities) to transform one side of the equation into the other side. If both sides are equal, then the identity is verified.

4. What are some common trigonometric identities?

Some common trigonometric identities include the Pythagorean identities (such as sin²𝜃 + cos²𝜃 = 1), the double angle identities (such as sin2𝜃 = 2sin𝜃cos𝜃), and the sum and difference identities (such as sin(𝜃 ± 𝜙) = sin𝜃cos𝜙 ± cos𝜃sin𝜙).

5. Why is it important to memorize trigonometric identities?

Memorizing trigonometric identities can save time when solving problems, as it eliminates the need to constantly look up the identities. It also helps with understanding the relationships between different trigonometric functions, making it easier to manipulate and solve equations involving them.

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