find-the-value-of-A-cos-pi-5-cos-2pi-5-cos-4pi-5-and-B-sin-pi-5-sin-2pi-5-sin-4pi-5-

Question Number 42508 by maxmathsup by imad last updated on 26/Aug/18

f i n d t h e v a l u e o f

A = c o s (\frac{π}{5}) . c o s (\frac{2 π}{5}) c o s (\frac{4 π}{5}) a n d B = s i n (\frac{π}{5}) s i n (\frac{2 π}{5}) s i n (\frac{4 π}{5}) .

Answered by math1967 last updated on 27/Aug/18

l e t \frac{π}{5} = θ ∴ 4 θ = π - θ

A = \frac{1}{2^{2} s i n θ} \times s i n 4 θ \times c o s 4 θ

= \frac{1}{4 s i n θ} \times s i n (π - θ) \times c o s 4 θ

= \frac{1}{4} \times c o s (π - θ) = - \frac{1}{4} c o s \frac{π}{5} = - \frac{\sqrt{5} + 1}{16}

Commented by rahul 19 last updated on 27/Aug/18

Nice!

Answered by math1967 last updated on 27/Aug/18

B = s i n θ s i n 2 θ s i n 4 θ [l e t θ = \frac{π}{5}]

B = s i n θ s i n 2 θ s i n (π - θ)

= {s i n}^{2} θ s i n 2 θ = \frac{1}{16} (10 - 2 \sqrt{5}) \times \frac{1}{4} \sqrt{10 + 2 \sqrt{5}}

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