X - n -3 -4 or x - m -tan -11-2- where m - n - I

The given equation is 2 tan^2 x+tan x 1=0 ⇒ (tan x+1)(2 tan x 1)=0 ⇒ tan x = 1 or tan x =1/2 ⇒ tan x =tan 3 π/4 or tan x =tan ( tan^ 11/2 ) ⇒ x =n π + ...

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Byju's Answer

Standard XI

Mathematics

Trigonometric Ratios for Sum of Two Angles

x = n π+3 π/4...

Question

$x = n π + \frac{3 π}{4}$ or $x = m π + t a n^{- 1} \frac{1}{2}$ , where m, $n \in I$

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Solution

The given equation is

$2 t a n^{2} x + t a n x - 1 = 0$

$\Rightarrow (t a n x + 1) (2 t a n x - 1) = 0$

$\Rightarrow t a n x = - 1$ or $t a n x = \frac{1}{2}$

$\Rightarrow t a n x = t a n \frac{3 π}{4}$ or $t a n x = t a n (t a n^{- 1} \frac{1}{2})$

$\Rightarrow x = n π + \frac{3 π}{4}$ or $x = m π + t a n^{- 1} \frac{1}{2}$ , where m, $n \in I .$

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x=nπ+3π4 or x=mπ+tan−112, where m, n∈I

The given equation is 2tan2x+tan x−1=0 ⇒(tan x+1)(2 tan x−1)=0 ⇒tan x=−1 or tanx=12 ⇒ tan x=tan 3π4 or tan x=tan(tan−112) ⇒x=nπ+3π4 or x=mπ+tan−112, where m, n∈I.

$x = n π + \frac{3 π}{4}$ or $x = m π + t a n^{- 1} \frac{1}{2}$ , where m, $n \in I$