Solving the Cos+SinTan/SinSec=Csc Equation

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SUMMARY

The discussion focuses on solving the equation (cos(x) + sin(x)tan(x))/(sin(x)sec(x)) = csc(x). Participants clarify the correct interpretation of the equation and emphasize the importance of proper punctuation and formatting for mathematical expressions. The conversation highlights the transition from the original equation to a more simplified form, addressing common mistakes in algebraic manipulation. Key insights include the necessity of using the least common multiple (LCM) in the numerator for accurate simplification.

PREREQUISITES
  • Understanding of trigonometric identities, specifically sin, cos, tan, sec, and csc.
  • Familiarity with algebraic manipulation techniques, including finding the least common multiple (LCM).
  • Basic knowledge of LaTeX for formatting mathematical expressions.
  • Ability to interpret and rewrite complex equations clearly.
NEXT STEPS
  • Study trigonometric identities and their applications in solving equations.
  • Practice algebraic manipulation involving LCM in trigonometric contexts.
  • Learn how to use LaTeX for writing mathematical equations effectively.
  • Explore common mistakes in algebraic simplification and how to avoid them.
USEFUL FOR

Students studying trigonometry, educators teaching algebraic manipulation, and anyone looking to improve their mathematical communication skills.

fouracres
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Homework Statement



cos+sintan/sinsec=csc

Homework Equations





The Attempt at a Solution


(cos+sin(sin/cos))/(sin/1/cos)
(cos+sin^2sincos)/(sin/cos)
(cos+sin^2sincos)X(cos/sin)
 
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How did you go from
(cos+sin(sin/cos))/(sin/1/cos) to
(cos+sin^2sincos)/(sin/cos) ?

The cosine should become the LCM in the numerator.
 
i think i multiplied sin by sin and cos i wouldn't doubt that i did it wrong can u correct me i really would love to fix this !
 
where were u saying cos shud become the LCM in the numerator?
 
fouracres said:
i think i multiplied sin by sin and cos i wouldn't doubt that i did it wrong can u correct me i really would love to fix this !

Have you ever heard of punctuation? The quote above appears to be three different sentences. Using periods at the ends of your sentences would make what you say easier to understand.

A similar problem exists with your first post (in addition to the omission of arguments of the functions shown):
cos+sintan/sinsec=csc

As you have written it, most people in this forum would interpret the above as:
cos(x) + \frac{sin(x)tan(x)}{sin(x)sec(x)} = csc(x)

I suspect that what you really meant, though, was this:
\frac{cos(x) +sin(x)tan(x)}{sin(x)sec(x)} = csc(x)

If you don't know how to use LaTeX, you can write the equation above like so:
(cos(x) +sin(x)tan(x))/(sin(x)sec(x))=csc(x)
 

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