Trouble Verifying Identity: Any Advice Welcome

In summary, the conversation discusses a problem with verifying a trigonometric identity. The participants share steps and solutions to help solve the problem. The final solution involves using the fundamental trigonometric identity and simplifying the equation to reach the correct answer. A new thread is opened for further discussion.
  • #1
powp
91
0
Hello All

I am having problems Verifying this identity

(COS A) / (1-SIN A) = SEC A + TAN A

I can get the RHS = (1 + SIN A)/COS A

But this does not equal the LHS

Any advice is welcome.

THanks
 
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  • #2
yes, you are right, now cross-multiply:

[tex]cos^2 a = (1 + sin a) (1 - sin a)[/tex]
[tex]cos^2 a = 1 - sin^2 a[/tex]
[tex]sin^2 a + cos^2 a = 1[/tex]
 
  • #3
sec A + tan A = (1/cosA) + sinA/cosA = (cosA + sinA*cosA)/(cosA)^2 =

cosA(1 + sinA)/(1-sin^2A) = cos A / (1 + sinA) :cool:
 
  • #4
does [tex]sin^2 a + cos^2 a = 1[/tex] verify the idenity?
 
  • #5
Divide the LHS top and bottom by cos A:

[tex]\frac{\cos A}{1-\sin A} = \frac{1}{\sec A - \tan A}[/tex]
[tex]=\frac{1}{(\sec A - \tan A)}\frac{(\sec A + \tan A)}{(\sec A + \tan A)}[/tex]
[tex]=\frac{\sec A + \tan A}{\sec^2 A - \tan^2 A}[/tex]

But

[tex]\sec^2 A - \tan^2 A = \frac{1 - \sin^2 A}{\cos^2 A} = 1[/tex]

So, the result follows.
 
  • #6
powp said:
Hello All

I am having problems Verifying this identity

(COS A) / (1-SIN A) = SEC A + TAN A

I can get the RHS = (1 + SIN A)/COS A

But this does not equal the LHS

Any advice is welcome.

THanks

Yes, it does: (1+ sin A)/cos A= 1/cos A+ sin A/cos A= sec A+ tan A.
 
  • #7
Thanks All Still kind of confused.

HallsofIvy: doesn't that just change back the RHS that I did??
 
  • #8
powp:

Does this help?

[tex]\frac{1 + \sin A}{\cos A} = \frac{(1 + \sin A)(1 - \sin A)}{\cos A(1 - \sin A)}[/tex]

[tex]=\frac{1 - \sin^2 A}{\cos A (1 - \sin A)}[/tex]

[tex]= \frac{\cos^2 A}{\cos A (1 - \sin A)}[/tex]

[tex]= \frac{\cos A}{1- \sin A}[/tex]
 
  • #9
powp said:
does [tex]sin^2 a + cos^2 a = 1[/tex] verify the idenity?

Yes that is perhaps the most fundamental of all trig identities. It's actually just Pythagoras Thm for a RHT with unit length hypotemus.
 
  • #10
Is this correct??

Hello All

I need to find all solutions to the following did i do it correct?

Sin 2x = 2Tan 2x

2Sinx Cosx = 2(2Tanx / 1-Tan^2x)

Sinx Cosx = (2(Sinx / Cosx)/(cos^2x-Sin^2x / Cos^2x))

Sinx Cosx = 2(Sinx / Cosx) X (Cos^2x / cos^2x-Sin^2x)

Cosx = 2 (Cosx / Cos^2x - Sin^2x)

1 = (2 / Cos^2x - Sin^2x)

Cos^2x - Sin^2x = 2

1 - Sinx^2 - Sin^2x = 2

2Sin^2x = -1
Sin^2x = -1/2

Sinx = -1/SQROOT(2)



Is this correct??
 
  • #11

1. How do I verify my identity?

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2. Why is my identity being verified?

Identity verification is a common security measure used to confirm that someone is who they claim to be. It may be required for various reasons, such as opening a new account, making a large financial transaction, or accessing sensitive information.

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In most cases, yes. Identity verification processes are designed to protect your personal information and prevent fraud. However, it's important to make sure you are providing information to a legitimate and trustworthy source. If you have any concerns, you can research the company or organization and contact them directly to verify the request.

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The length of the identity verification process can vary depending on the specific situation. Some verifications may only take a few minutes, while others may take several days. It's important to be patient and follow any instructions provided to ensure a smooth and successful verification process.

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