The general value of θ satisfying the equation tan θ+ tan ((π/2)-θ) (- b ± √ b 2-4 ac /2 a )=2, is

Question

The general value of θ satisfying the equation tan θ+ tan ((π/2)-θ) (- b ± √ b 2-4 ac /2 a )=2, is (A) n π ± (π/4) (B) n π+(π/4) (C) 2 n π ± (π/4) (D) n π+(-1) n (π/4)

Tardigrade Admin · Accepted Answer

tan θ+ tan ((π/2)-θ)=2 ⇒ tan θ+(1/ tan θ)=2 ⇒ tan 2 θ-2 tan θ+1=0 ⇒ tan θ=1= tan (π/4) ⇒ θ= n π+(π/4)

Q. The general value of $θ$ satisfying the equation $tan θ + tan (\frac{π}{2} - θ) \frac{- b \pm b ^{2} - 4 a c}{2 a} = 2$ , is

$nπ \pm \frac{π}{4}$

$nπ + \frac{π}{4}$

$2 nπ \pm \frac{π}{4}$

$nπ + (- 1)^{n} \frac{π}{4}$

$tan θ + tan (\frac{π}{2} - θ) = 2$
$\Rightarrow tan θ + \frac{1}{t a n θ} = 2$
$\Rightarrow tan^{2} θ - 2 tan θ + 1 = 0$
$\Rightarrow tan θ = 1 = tan \frac{π}{4}$
$\Rightarrow θ = nπ + \frac{π}{4}$

Q. The general value of θ satisfying the equation tanθ+tan(2π​−θ)2a−b±b2−4ac​​=2, is

nπ±4π​

nπ+4π​

2nπ±4π​

nπ+(−1)n4π​