A) 0
B) \[2(x+y+z)\]
C) \[\frac{3\pi }{2}\]
D) \[\frac{3\pi }{2}+x+y+z\]
Correct Answer: A
Solution :
[a] \[\tan (ta{{n}^{-1}}x+ta{{n}^{-1}}y+ta{{n}^{-1}}z)\] \[-\cot (co{{t}^{-1}}x+co{{t}^{-1}}y+co{{t}^{-1}}z)\] \[=\tan (ta{{n}^{-1}}x+ta{{n}^{-1}}y+ta{{n}^{-1}}z)\] \[-\cot \left( \frac{\pi }{2}-{{\tan }^{-1}}x+\frac{\pi }{2}-{{\tan }^{-1}}y+\frac{\pi }{2}-{{\tan }^{-1}}z \right)\] \[\left( \because {{\tan }^{-1}}x+{{\cot }^{-1}}x=\frac{\pi }{2} \right)\] \[=\tan (ta{{n}^{-1}}x+ta{{n}^{-1}}y+ta{{n}^{-1}}z)\] \[-\cot \{3\pi /2-(ta{{n}^{-1}}x+ta{{n}^{-1}}y+ta{{n}^{-1}}z)\] \[=\tan (ta{{n}^{-1}}x+ta{{n}^{-1}}y+ta{{n}^{-1}}z)\] \[-\tan (ta{{n}^{-1}}x+ta{{n}^{-1}}y+ta{{n}^{-1}}z)=0\]
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