Verifying Trig Identities: csc(A-B)=secB

In summary, the conversation is about verifying the identity csc(A-B)=secB / (sinA-cosAtanB) and the person is stuck on the first step of the solution. They are trying to put the equation in terms of sin and cos, but have made a mistake and are asking for help.
  • #1
gunnar14
1
0

Homework Statement


Verify that each equation is an identity- directions
Problem- csc(A-B)=secB
---------------- <<< divide bar
sinA-cosAtanB

Homework Equations



well i tried to put in terms of sin cos and I've gotten stuck

The Attempt at a Solution



i started off by disributing i.e.>> cscA-cscB=secB/sinA-cosAtanB
next i changed tan to sin/cos and canceled out cos so i was left with cscA-cscB=sec/sinA-sinB

changed csc to 1/sinA-1/sinB=sec/sinA-sinB

changed sec to 1/cos so i flipped and multiplied 1/sinA-sinB and got 1/sinA-1/sinB= 1/sincosA-sincosB and I am stuck here... help please
 
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  • #2
gunnar14 said:

Homework Statement


Verify that each equation is an identity- directions
Problem- csc(A-B)=secB
---------------- <<< divide bar
sinA-cosAtanB

Homework Equations



well i tried to put in terms of sin cos and I've gotten stuck

The Attempt at a Solution



i started off by disributing i.e.>> cscA-cscB=secB/sinA-cosAtanB
next i changed tan to sin/cos and canceled out cos so i was left with cscA-cscB=sec/sinA-sinB

changed csc to 1/sinA-1/sinB=sec/sinA-sinB

changed sec to 1/cos so i flipped and multiplied 1/sinA-sinB and got 1/sinA-1/sinB= 1/sincosA-sincosB and I am stuck here... help please
Just to be clear, the problem you're trying to solve is to verify the identity

[tex]\csc(A-B)=\frac{\sec B}{\sin A-\cos A \tan B}[/tex]

right? Your post is kind of hard to read.

Your very first step is wrong because [itex]\csc(A-B) \ne \csc A - \csc B[/itex]. Try writing it in terms of sin(A-B) first and go from there.
 

Related to Verifying Trig Identities: csc(A-B)=secB

1. What is the purpose of verifying trig identities?

The purpose of verifying trig identities is to ensure that the given expression is equivalent to the original expression. This is important in solving trigonometric equations and simplifying complex expressions.

2. How do you verify a trig identity?

To verify a trig identity, you must manipulate the given expression using algebraic and trigonometric identities until it matches the original expression. This involves using properties such as the Pythagorean identities and double angle identities.

3. What is the difference between proving and verifying a trig identity?

Proving a trig identity involves starting with one side of the equation and using algebraic and trigonometric manipulations to reach the other side. Verifying a trig identity, on the other hand, involves checking if the given expression is equivalent to the original expression.

4. How do you verify the identity csc(A-B)=secB?

To verify the identity csc(A-B)=secB, you can use the double angle identity for sine, which states that csc(2x)=secx. By substituting 2x for A-B, we get csc(A-B)=sec(A-B). Then, using the reciprocal property of trigonometric functions, we can rewrite this as secB=csc(A-B), verifying the given identity.

5. Why is it important to verify trig identities?

It is important to verify trig identities because it ensures the accuracy and validity of mathematical expressions involving trigonometric functions. This is especially important when solving equations or simplifying complex expressions, as an error in a trig identity can lead to incorrect solutions and results.

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