How can I prove the trig identity sinxcosxsec^2x = tanx?

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Homework Help Overview

The discussion revolves around proving the trigonometric identity sin(x)cos(x)sec²(x) = tan(x). Participants are exploring various approaches to manipulate the equation using trigonometric identities.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to manipulate the equation using the identity sec²(x) = tan²(x) + 1, but expresses uncertainty about the validity of their steps. Other participants suggest rewriting secant squared as 1/cos²(x) and simplifying the expression, while some provide definitions of trigonometric functions.

Discussion Status

Participants are actively engaging with the problem, offering different perspectives and methods for simplification. There is no explicit consensus on a single approach, but some guidance has been provided regarding rewriting and simplifying the terms involved.

Contextual Notes

There is a mention of uncertainty regarding the correctness of the original poster's manipulations, indicating potential gaps in understanding or application of trigonometric identities.

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1. How do I prove sinxcosxsec^2x=tanx



Homework Equations


sec^2x = tan^2x + 1


The Attempt at a Solution




sinxcosx(tan^2x + 1)
tan^2xsinxcosx +sinxcosx
sin^2x/cos^2x*sinxcosx + sinxcosx - is this valid?

I'm not sure what I've done is even correct - but it doesn't seem to be going anywhere helpful?

 
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Rewrite secant squared as 1/cos squared. The you'll have (sincos)/(coscos). Cancel cosines and you're done. I'll edit this from my computer and add arguments later!
 
secant = 1/cosine
cosecant = 1/sine
cotangent = 1/tangent
 
iRaid said:
secant = 1/cosine
cosecant = 1/sine
cotangent = 1/tangent

SOHCAHTOA. qed
 
Many thanks for your help
 
The Chaz said:
SOHCAHTOA. qed
Wasn't that Lewis and Clark's indian guide?
 
No, this is the one that's featured on the new US coins ;)
 

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