আমাদের টেলিগ্রাম চ্যানেলে যুক্ত হোন

Prove that,$\sin \left(\frac{2\pi }{3} + \theta \right) – sin\left(\frac{2\pi }{3} – \theta \right) + sin\theta$ = 0

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Prove that, $\sin \left(\frac{2\pi }{3} + \theta \right) – sin\left(\frac{2\pi }{3} – \theta \right) + sin\theta$ = 0

$L\ldotp H\ldotp S\sin \left(\frac{2\pi }{3} + \theta \right) – sin\left(\frac{2\pi }{3} – \theta \right) + sin\theta$

= $2cos\left(\frac{\frac{2\pi }{3} + \theta + \frac{2\pi }{3} – \theta }{2}\right)sin\left(\frac{\frac{2\pi }{3} + \theta – \frac{2\pi }{3} + \theta }{2}\right) + sin\theta$

= $2cos\left(\frac{4\pi }{6}\right)sin\theta + sin\theta$

= $2cos\frac{2\pi }{3}sin\theta + sin\theta$

= $2cos\left(\pi – \frac{\pi }{3}\right)\sin \theta + sin\theta$

= – $2cos\frac{\pi }{3}sin\theta + sin\theta$

= – $2 \times \frac{1}{2} \times sin\theta + sin\theta$

= – $sin\theta + sin\theta$

= 0 = $R\ldotp H\ldotp S$ [Proved]

আরও দেখুন

  1. Prove That, $sec\left(\frac{\pi }{4} + \theta \right)\sec \left(\frac{\pi }{4} – \theta \right)$ = $2sec2\theta$
  2. If sinθ + sinΦ=a and cos θ +cosΦ=b prove that $tan\frac{\theta  – \phi }{2}$ =  $\pm \sqrt{\frac{4 – a^2 – b^2}{a^2 + b^2}}$
  3. ProveThat,$\tan\theta tan\left(\frac{\pi }{3}+\theta \right)\tan \left(\frac{\pi }{3}-\theta \right)$=$tan3\theta$
  4. if a cosφ=b cosθ then show that atanθ+btanφ=(a+b) tan$\frac{{\mathrm{\theta}} + {\mathrm{\phi}}}{2}$
  5. Prove that, $cos(\alpha + \beta ) + sin(\alpha – \beta )$ = $2sin\left(\frac{\pi }{4} + \alpha \right)\cos \left(\frac{\pi }{4} + \beta \right)$

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