Simplifying/Proving a Trigonometric Question

I finally got it.In summary, the conversation discusses how to prove the equation secA(1+sinA) = (1+sinA+cosA)/(1-sinA+cosA) using various trigonometric identities. It is suggested to either use the double angle formula for A/2 or multiply both sides by the conjugate (1-sinA+cosA) to simplify the equation. The conversation ends with the acknowledgement that the solution has been achieved.
  • #1
BlackHole213
34
0

Homework Statement



Prove:

secA(1+sinA) = (1+sinA+cosA)/(1-sinA+cosA)


Homework Equations



I have the following equations:

sin2x + cos2x = 1
1 + tan2x = sec2x
1 + cot2x = csc2x
sin(A+B) = sinAcosB + cosAsinB
sin(A-B) = sinAcosB - cosAsinB
cos(A+B) = cosAcosB - sinAsinB
cos(A-B) = cosAcosB + sinAsinB
sin(2A) = 2sinAcosA
cos(2A) = cos2 - sin2A

These formulas are all I have, but as this is a bonus question, there might be other formulas which I am unaware of.


The Attempt at a Solution



I looked at https://www.physicsforums.com/showthread.php?t=423847 to see if I could get inspiration to achieve an answer. I've tried simplifying the left side to (1+sinA)/cosA and then I attempted to see if I could get the right hand side to equal that. I've multipled the RHS by (1+sinA+cosA)/(1+sinA+cosA), (1-sinA+cosA)/(1-sinA+cosA) and I've tried multiplying the RHS by its reciprocal and the LHS by cosA/(1+sinA). In that last attempt, I achieved an answer of 1=1, but I have a feeling that is incorrect and I'll need at least one trigonometric function in the solution.

If anyone wants to see the work that I've done in each attempt, just tell me and I'll post it.

Thanks for the assistance.
 
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  • #3
Always remember to multiply by the conjugate.

[PLAIN]http://img337.imageshack.us/img337/1976/50453339.jpg [Broken]
 
Last edited by a moderator:
  • #4
Thank you, both of you.
 

What is the process for simplifying a trigonometric question?

The process for simplifying a trigonometric question involves using trigonometric identities and properties to reduce the given expression into a simpler form. This can include using the Pythagorean identities, sum and difference identities, and double angle identities.

How do I prove a trigonometric identity?

To prove a trigonometric identity, you must start with one side of the equation and manipulate it using known identities and algebraic techniques until you reach the other side of the equation. If both sides are equal after simplification, the identity is proven.

What are the most commonly used trigonometric identities?

The most commonly used trigonometric identities include the Pythagorean identities (sin^2x + cos^2x = 1), the sum and difference identities (sin(x+y) = sinxcosy + cosxsiny), and the double angle identities (sin2x = 2sinxcosx).

How can I check my work when simplifying a trigonometric question?

You can check your work by substituting in different values for the variables in the original expression and the simplified expression. If both expressions give the same result, then your simplification is correct.

What are some tips for simplifying trigonometric expressions?

Some tips for simplifying trigonometric expressions include looking for common factors to factor out, using the reciprocal identities to change the form of the expression, and using the unit circle to help visualize the values of trigonometric functions at different angles.

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