If the general solution of the equation tan 3-1- is given by -n-3- where n- and -0- -6- then - equals-

We know the general solution of the equation of the form nbsp;tan nbsp;θ=tan nbsp;α, is given by nbsp;θ=nπ+α. Now, we can solve the equation as : tan ...

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Standard XIII

Mathematics

General Solution of tan theta = tan alpha

If the genera...

Question

$If the general solution of the equation tan 3 θ = - 1, is given by θ = \frac{n π}{3} - α, where n \in Z and α \in (0, \frac{π}{6}], then α equals$
.

\frac{π}{6}

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\frac{π}{12}

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\frac{π}{15}

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Solution

The correct option is B $\frac{π}{12}$
We know the general solution of the equation of the form $tan θ = tan α$ , is given by $θ = n π + α .$
Now, we can solve the equation as :
$tan 3 θ = - 1 \Rightarrow tan 3 θ = tan (- \frac{π}{4}) \Rightarrow 3 θ = n π + (- \frac{π}{4}), n \in Z \Rightarrow θ = \frac{nπ}{3} + (- \frac{π}{12}), n \in Z \Rightarrow θ = \frac{nπ}{3} - \frac{π}{12}, n \in Z .$
thus, comparing with the solution we get $α = \frac{π}{12} .$

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If the general solution of the equation tan 3θ=−1, is given by θ=nπ3−α, where n∈Z and α∈(0, π6], then α equals .

$If the general solution of the equation tan 3 θ = - 1, is given by θ = \frac{n π}{3} - α, where n \in Z and α \in (0, \frac{π}{6}], then α equals$
.