Question-208437

Question Number 208437 by efronzo1 last updated on 16/Jun/24

Answered by som(math1967) last updated on 16/Jun/24

a = s i n 84 + c o s 66

\Rightarrow a = s i n 84 + s i n 24

\Rightarrow a = 2 s i n 54 c o s 30

∴ a = 2 \times \frac{\sqrt{5} + 1}{4} \times \frac{\sqrt{3}}{2} = \frac{\sqrt{3} (\sqrt{5} + 1)}{4}

b = s i n 48 - s i n 12

\Rightarrow b = 2 s i n 18 . c o s 30 = \frac{\sqrt{3} (\sqrt{5} - 1)}{4}

a b = \frac{3 (5 - 1)}{4 \times 4} = \frac{3}{4}

\frac{a}{b} = \frac{\sqrt{5} + 1}{\sqrt{5} - 1}

\Rightarrow \frac{a + b}{a - b} = \frac{2 \sqrt{5}}{2} = \sqrt{5}

{(\frac{a + b}{a - b})}^{8 a b} = 5^{\frac{1}{2} \times 8 \times \frac{3}{4}} = 5^{3}

Commented by efronzo1 last updated on 16/Jun/24

= 5^{3}

Commented by som(math1967) last updated on 16/Jun/24

y e s