If 0<θ<8π , show that 2+2+2+2cos4θ =2cos(θ/2).

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If $0 < θ < \frac{π}{8}$ , show that $2 + 2 + 2 + 2 cos 4 θ = 2 cos (θ /2) .$

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Mila Discussed

0 < θ < \frac{π}{8}

, show that

2 + 2 + 2 + 2 cos 4 θ = 2 cos (θ /2) .

7 mins ago

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7 mins ago

2 + 2 + 2 + 2 cos 4 θ

= 2 + 2 + 2 (1 + cos 4 θ)

= 2 + 2 + 2 (1 + 2 cos^{2} 2 θ - 1)

= 2 + 2 + 4 cos^{2} 2 θ

= 2 + 2 + 2 cos 2 θ

= 2 + 2 (1 + cos 2 θ)

= 2 + 4 cos^{2} θ

= 2 + 2 cos θ

= 2 (1 + cos θ)

= 4 cos^{2} \frac{θ}{2}

= 2 cos \frac{θ}{2}

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