If tan - -2-then the values of x which satisfy the relationtan x-1-2are 0 x2- and0 -2

We have tan α =2 ⇒ cot α = 1/2 So, we are given tan x = 1/2= cot α or tan x = cot α We know tan π/2 α = tan ( 3π/2 α ) =cot α ⇒ tan x =tan ( π/2 α ...

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Standard XIII

Mathematics

General Solution of tan theta = tan alpha

If tan α =2,t...

Question

If tan $α = 2$ ,then the values of x which satisfy the relation

$t a n x = \frac{1}{2} a r e$ $0 < x <$ $2 π a n d$ $0 < α <$ $\frac{π}{2}$

$\frac{π}{2} + α$

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$π + α$

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$\frac{3 π}{2} - α$

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$\frac{π}{2} - α$

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Solution

The correct option is D
$\frac{π}{2} - α$

We have tan $α = 2$

$\Rightarrow c o t α = \frac{1}{2}$

So, we are given $t a n x = \frac{1}{2} = c o t α o r t a n x = c o t α$

We know tan $\frac{π}{2} - α = t a n (\frac{3 π}{2} - α) = c o t α$

$\Rightarrow t a n x = t a n (\frac{π}{2} - α) o r t a n (\frac{3 π}{2} - α)$
$\Rightarrow x = \frac{π}{2} - α o r x = \frac{3 π}{2} - α$

We considered on $\frac{π}{2}$ - α and $\frac{3 π}{2} - α$ because we want $0 < x < 2 π$

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If tan α=2,then the values of x which satisfy the relation tanx=12are 0<x<2π and 0<α<π2

The correct option is D π2−α We have tan α=2 ⇒cotα=12 So, we are given tanx=12=cot α or tanx=cotα We know tan π2−α=tan(3π2−α)=cotα ⇒tanx=tan(π2−α)or tan(3π2−α) ⇒x=π2−αorx=3π2−α We considered on π2 - α and 3π2−αbecause we want 0<x<2π

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