sin²(x) +cos²(x)=1 Proof

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#calculus #maths #proof #trigonometry #trending
Welcome to our concise and clear tutorial on proving sin²(x) +cos²(x)=1! In this video, we'll walk you through a step-by-step proof and provide a deep understanding of this trig identity.
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This proof relies upon Pythagorus' theorem. So to be a rigorous proof you now need to prove that (without using Sin^2 x + Cos^2 x =1).

RylanceStreet
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I never knew! That is so crazy! Excellent video! I really enjoyed this!

vortex
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cos(a-b)=sin(a)*sin(b)+cos(a)*cos(b), cos(a-a)=sin(a)*sin(a)+cos(a)*cos(a),

victor
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Usually, for a complex number z, sin(z) is defined as [exp(iz)-exp(-iz)]/(2i) and cos(z) is defined as [exp(iz)+exp(-iz)]/2. Using the identity exp(x+y) = exp(x) * exp(y), we may calculate that sin(z)^2 + cos(z)^2 = 1.

zswu
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Sin² x + Cos² x = ?
x = 0° - k.360°
e.g : 0°, 30°, 45°, 60°, 90°

Sin² 0° + Cos² 0° = 0 + 1 = 1
Sin² 30° + Cos² 30° = (½)² + (½√3)² = 1
Sin² 45° + Cos² 45° = (½√2)² + (½√2)² = 1
Sin² 60° + Cos² 60° = (½√3)² + (½)² = 1
Sin² 90° + Cos² 90° = 1 + 0 = 1

So Sin² x + Cos² x = 1

andryvokubadra
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this is true in 0<x<90 range ?not for all the degrees in |R 🙄yes or no 🤕

yaka
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Hmm a british explaining trignometry, what was i serching for 😅

thunderpokemon