MHB Finding an Alternative Solution to Doubtful Numerator Steps

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SUMMARY

The discussion centers on finding alternative solutions to the equation involving trigonometric identities, specifically $\sin^2x + \cos^2x = 1$. Participants explore the transformation of this identity into $\sin^2x - i^2 \cos^2x = 1$ and its implications when substituting $x = \frac{2\pi}{9}$. The conversation emphasizes the importance of understanding complex numbers in trigonometric contexts and encourages further exploration of alternative methods to derive the numerator steps.

PREREQUISITES
  • Understanding of trigonometric identities, specifically $\sin^2x + \cos^2x = 1$
  • Familiarity with complex numbers and their properties
  • Basic knowledge of substitution methods in trigonometric equations
  • Experience with angle measures in radians
NEXT STEPS
  • Research complex number applications in trigonometry
  • Explore alternative proofs of trigonometric identities
  • Learn about substitution techniques in solving trigonometric equations
  • Investigate the implications of using $x = \frac{2\pi}{9}$ in various trigonometric contexts
USEFUL FOR

Mathematicians, students studying trigonometry, and anyone interested in exploring complex numbers within trigonometric identities.

DaalChawal
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Doubt in marked step(Numerator) that how it came from first?
Is there any alternative solution for this?
 
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We generally have $\sin^2x + \cos^2 x=1$.
So $\sin^2x - i^2 \cos^2 x=1$ as well.
Now substitute $x=\frac{2\pi}{9}$. 🤔
 
Thanks
 

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