If x sin a + y sin 2 a + z sin 3 a = sin 4 a , x sin b + y sin 2 b + z sin 3 b = sin 4 b , x sin c + y sin 2 c + z sin 3 c = sin 4 c , then the roots of the equation t 3 − ( 2 z ) t 2 − ( 4 y + 2

Question

If x sin a + y sin 2 a + z sin 3 a = sin 4 a , x sin b + y sin 2 b + z sin 3 b = sin 4 b , x sin c + y sin 2 c + z sin 3 c = sin 4 c , then the roots of the equation t 3 − ( 2 z ​ ) t 2 − ( 4 y + 2 ​ ) t + ( 8 z − x ​ ) = 0 , a , b , c  = nπ , are

TestHub · Accepted Answer

x sin a + y sin 2 a + z sin 3 a = sin 4 a ⇒ 8 cos 3 a − 4 z cos 2 a − ( 2 y + 4 ) cos a + ( z − x ) = 0 , i.e. cos a is a root of the given equation. The same holds for b and c .

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

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