How Do You Solve This Complex Trigonometry Homework Problem?

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SUMMARY

The discussion revolves around solving the trigonometric equation tan(x) + cot(x) = 4 and evaluating the expression cos²(x) + sin²(x) + tan²(x) + cot²(x) + csc²(x) + sec²(x). Participants clarify that tan²(x) + cot²(x) can be derived as 14 after squaring both sides of the initial equation. The final evaluation leads to the conclusion that the answer is 31, achieved by substituting values derived from the original equation.

PREREQUISITES
  • Understanding of trigonometric identities, specifically tan(x), cot(x), csc(x), and sec(x).
  • Familiarity with algebraic manipulation of equations, including squaring both sides.
  • Knowledge of basic trigonometric equations and their transformations.
  • Ability to simplify expressions involving sine and cosine functions.
NEXT STEPS
  • Study the derivation of trigonometric identities, focusing on tan²(x) and cot²(x).
  • Learn how to manipulate and solve trigonometric equations effectively.
  • Explore the applications of trigonometric identities in solving complex equations.
  • Practice evaluating expressions involving multiple trigonometric functions.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their problem-solving skills in trigonometric equations.

  • #31
Exactly what I was saying. You've left nothing to the imagination which is why you've given the solution indirectly and this makes your fear of not giving the entire solution to abide by PF rules futile.

I think trigonometry is very difficult part for noobs. That's the only reason.
 
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  • #32
snshusat161 said:
I mean you want to show that I'm not following PF rules
I didn't mean to provoke you, I was trying to show you why you weren't actually obeying the PF rules. If you disagree with me, then by all means, ask a moderator if your method of helping is within the guidelines of the rules.
snshusat161 said:
I think trigonometry is very difficult part for noobs. That's the only reason.
This doesn't mean we should be solving all the trigonometry and leaving just the algebra part up to them to solve, because they're not as "noob" at algebra.
Also, the OP isn't as bad at trigonometry as you make him out to be :-p And we've all been there at one stage in our lives. Believe it or not, I too was a noob at trigonometry about 2 years back.
 
  • #33
Okay, I'll take care next time I post.
 
  • #34
I myself had an infraction when I started off in this forum so don't worry, it'll quickly become clear to you what is acceptable and what isn't. Most if not all high-count poster (I'll say 500 and above) give acceptable homework help. You should follow their lead :wink:
 

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