Question-217631

Question Number 217631 by mnjuly1970 last updated on 17/Mar/25

Commented by mnjuly1970 last updated on 17/Mar/25

y e s . {t h a t}^{'} s r i g h t . t h a n k s a l o t s i r

Answered by maths2 last updated on 17/Mar/25

a = \frac{1}{a^{'}} = \frac{1}{s i n (10)}; b = \frac{1}{s i n (70)} = \frac{1}{b^{'}}

c = \frac{1}{s i n (50)} = \frac{1}{c^{'}}

a^{2} + b^{2} + c^{2} = \frac{1}{{s i n}^{2} (10)} + \frac{1}{{s i n}^{2} (70)} + \frac{1}{{s i n}^{2} (50)}

s i n (10.3) = s i n (30); s i n (3.70) = s i n (210) = - s i n (30)

s i n (3.50) = s i n (150) = s i n (30)

s i n (10); s i n (50); - s i n (70) r o o t o f

s i n (3 x) = \frac{1}{2} \Leftrightarrow - {s i n}^{3} (x) + 3 s i n (x) (1 - {s i n}^{2} (x)) = \frac{1}{2}

\Leftrightarrow {s i n}^{3} (x) - \frac{3}{4} s i n (x) + \frac{1}{8} = 0

\frac{1}{a^{' 2}} + \frac{1}{b^{' 2}} + \frac{1}{c^{' 2}} = \frac{{(a^{'} b^{'} + b^{'} c^{'} + c^{'} a^{'})}^{2} - 2 a^{'} b^{'} c^{'} (a^{'} + b^{'} + c^{'})}{{(a^{'} b^{'} c^{'})}^{2}}

= \frac{{(- \frac{3}{4})}^{2}}{{(- \frac{1}{8})}^{2}} = 36 c o r r e c t e a n s w e r i s C

Facebook Tweet Pin