A) \[\tan {{20}^{o}}+\tan {{50}^{o}}\]
B) \[2\tan {{20}^{o}}+\tan {{50}^{o}}\]
C) \[\tan {{20}^{o}}+2\tan {{50}^{o}}\]
D) \[2\tan {{20}^{o}}+2\tan {{50}^{o}}\]
Correct Answer: C
Solution :
\[\sec {{50}^{o}}+\tan {{50}^{o}}\] Þ \[\tan ({{70}^{o}}-{{20}^{o}})=\frac{\tan {{70}^{o}}-\tan {{20}^{o}}}{1+\tan {{70}^{o}}\tan {{20}^{o}}}\] Þ \[\tan {{50}^{o}}+\tan {{70}^{o}}\tan {{20}^{o}}\tan {{50}^{o}}=\tan {{70}^{o}}-\tan {{20}^{o}}\] Þ \[\tan {{50}^{o}}+\tan {{50}^{o}}=\tan {{70}^{o}}-\tan {{20}^{o}}\] \[[\,\because \tan {{70}^{o}}=\cot {{20}^{o}}]\] Þ \[2\tan {{50}^{o}}+\tan {{20}^{o}}=\tan {{70}^{o}}\] Þ \[2\tan {{50}^{o}}+\tan {{20}^{o}}=\tan {{50}^{o}}+\sec {{50}^{o}}\].
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