A) 1
B) 0
C) \[\tan 50{}^\circ \]
D) None of these
Correct Answer: B
Solution :
[b]:\[\tan 20{}^\circ +2\tan 50{}^\circ -\tan 70{}^\circ \] \[=\frac{\sin 20{}^\circ }{\cos {{20}^{o}}}-\frac{\sin 70{}^\circ }{\cos {{70}^{o}}}+2\tan {{50}^{o}}\] \[=\frac{\sin 20{}^\circ \cos {{70}^{o}}-\cos {{20}^{o}}\sin {{70}^{o}}}{cos{{20}^{o}}\cos {{70}^{o}}}+2\tan {{50}^{o}}\] \[=\frac{\sin ({{20}^{o}}-{{70}^{o}})}{\frac{1}{2}[cos({{70}^{o}}+{{20}^{o}})+\cos ({{70}^{o}}-{{20}^{o}})]}+2\tan {{50}^{o}}\] \[=\frac{2\sin (-{{50}^{o}})}{\cos {{90}^{o}}+\cos {{50}^{o}}}+2\tan {{50}^{o}}\] \[=\frac{-2\sin {{50}^{o}}}{0+\cos {{50}^{o}}}+2\tan {{50}^{o}}\] \[=-2\tan {{50}^{o}}+2\tan {{50}^{o}}=0\]
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