Some trigonometric equations are given in Column-I and some or whole of their solutions are give....
Some trigonometric equations are given in Column-I and some or whole of their solutions are given in Column-II. Match these.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|l|}{ Column-I } & \multicolumn{2}{|c|}{ Column-II } \\
\hline (A) & \begin{tabular}{l}
If \( 0 \leq x, y \leq 2 \pi \) and \( \alpha \) and \( \beta \) \\
are solutions of the equation \\
\( \sin x+\sin y=2 \), then \( \alpha+\beta \) is
\end{tabular} & (P) & \( \frac{\pi}{3} \) \\
\hline (B) & \begin{tabular}{l}
If \( 4 \cos ^{2} x+4 \cos x-3=0 \), then \\
the value of \( x \) in the interval \\
{\( [0,2 \pi] \) is }
\end{tabular} & (Q) & \( \frac{5 \pi}{3} \) \\
\hline (C) & \begin{tabular}{l}
The solution of the equation \\
\( 2 \sin ^{2} x+(4-\sqrt{3}) \sin x-2 \sqrt{3} \) \\
\( =0 \) in the interval \( [0, \pi] \) is
\end{tabular} & (R) & \( \frac{2 \pi}{3} \) \\
\hline (D) & \begin{tabular}{l}
Solution of the equation \\
\( \sqrt{3}-\tan x=\tan (\pi / 3-x) \) \\
are
\end{tabular} & (S) & \( \frac{\pi}{2} \) \\
\hline & & (T) & \( \pi \) \\
\hline
\end{tabular}
(1) A-T; B-P, Q; C-P, R; D-P, T
(2) A-P; B-Q; C-P, S; D-Q, R
(3) A-Q, P; B-R, S; C-P, Q; D-T
(4) A-Q, R; B-S, T; C-P, Q, Q; D-S
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