For homework, we were asked to prove that [tex] \cos^2 \theta + \sin^2 \theta = 1 [/tex] is true for all angles [tex] \theta [/tex]. Can someone please take a look at these and let me know if they are acceptable. I'm pretty sure the second one works, but I'm not sure of the first one, mainly because the premise of the proof is derived from the identity I'm trying to prove. Is that allowable or is that a circular argument? Thanks in advance.(adsbygoogle = window.adsbygoogle || []).push({});

P.S. I'm still trying to get used to LATEX, so please forgive me if I've screwed anything up.

PROOF #1:

Given that: [tex] \tan^2 \theta + 1= \sec^2 \theta [/tex]

[tex] \frac{ sin^2 \theta}{cos^ 2 \theta} + 1= \frac {1}{cos^ 2\theta} [/tex]

multiplying by: [tex] \cos^ 2 \theta [/tex]

I get:

[tex] \sin^2 \theta + \cos^2 \theta =1 [/tex]

PROOF #2:

(First I drew a right triangle, labeling x, y, r, and [tex] \theta [/tex] ).

Given that: [tex] x^2 + y^2 = r^2[/tex]

dividing by: [tex] r^2 [/tex]:

[tex] \frac {x^2} {r^2} + \frac {y^2} {r^2} = \frac {r^2}{r^2} [/tex]

I get:

[tex] \cos^2 \theta + \sin^2 \theta = 1[/tex].

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# Pythagorean Identity Proofs?

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