If arctan(tanα) = -2π/7 Which of the following values can have α have?
a) -9π/7
b) 2π/7
c) -5π/7
d) 5π/7
Answer:-
arctan(x) is same as tan-1(x)
Graph of tan-1("x" )
We have given "tan^{-1}tan(\\alpha)=\\frac{-2\\pi}{7}"
According to question , we can have values of "\\alpha" as follows
(1) "y=\\alpha"
(2)"y=\\alpha-\\pi"
(3)"y=\\alpha+\\pi"
We got
"\\alpha=\\frac{-2\\pi}{7} from (1)"
"\\alpha=\\frac{-9\\pi}{7} \\ from(2)"
"\\alpha=\\frac{5\\pi}{7} \\ from (3)"
So , in the given question options (a) and (d) are possible.
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