Question

cos²(π/10)+cos²(2π/5)++cos²(3π/5)+cos²(9π/10)=2​

Answer 1

Answer:

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Step-by-step explanation:

$to \: prove = \\ cos {}^{2} \frac{\pi}{10} + cos {}^{2} \frac{2\pi}{5} + cos {}^{2} \frac{3\pi}{5} + cos {}^{2} \frac{9\pi}{10} = 2 \\ \\ considering \: LHS \\ \\ = cos {}^{2} \frac{\pi}{10} + cos {}^{2} \frac{2\pi}{5} + cos {}^{2} \frac{3\pi}{5} + cos {}^{2} \frac{9\pi}{10} \\ \\ = cos {}^{2} \: \frac{\pi + 9\pi}{10} + cos {}^{2} \: \frac{2\pi + 3\pi}{5} \\ \\ = cos {}^{2} \: \frac{10\pi}{10} + cos {}^{2} \: \frac{5\pi}{5} \\ \\ = cos {}^{2} \: \pi + cos {}^{2} \: \pi \\ \\ = 2.cos {}^{2} \: \pi \\ \\ we \: know \: that \\ cos \: \pi = - 1 \\ \\ = 2( - 1) {}^{2} \\ \\ = 2 \times 1 \\ \\ = 2 \\ \\ thus \: LHS=RHS \\ \\ hence \: proved$