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Match the following Trignometric ratios with the equations whose one of the roots is given
Column-I Column-II
A $\cos 20^{\circ}$ P $x^{3} - 3 x^{2} - 3 x + 1 = 0$
B $\sin 10^{\circ}$ Q $32 x^{5} - 40 x^{3} + 10 x - 1 = 0$
C $T a n 15^{\circ}$ R $8 x^{3} - 6 x - 1 = 0$
D $\sin 6^{\circ}$ S $8 x^{3} - 6 x + 1 = 0$

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$A \to R, B \to S, C \to P, D \to Q$

$A \to R, B \to P, C \to S, D \to Q$

$A \to R, B \to P, C \to Q, D \to S$

$A \to P, B \to R, C \to Q, D \to S$

answer is A.

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Detailed Solution

$A - R, B - S, C - P, D - P$

A. $A = 20^{0} \Rightarrow 3 A = 60^{0} \Rightarrow C O S 3 A = \frac{1}{2}$

B. $A = 20^{0} \Rightarrow 3 A = 60^{0} \Rightarrow 8 x^{3} - 6 x - 1 = 0$ where $x = \cos 20^{0}$

C. $A = 10^{0} \Rightarrow \sin 3 A = \frac{1}{2} \Rightarrow 8 x^{3} - 6 x - 1 = 0$ where $x = \sin 10^{0}$

D. $A = 6^{0} \Rightarrow \sin 5 A = \frac{1}{2} \Rightarrow 32 x^{5} - 40 x^{3} + 10 x - 1 = 0$ where x=sin 6

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