The most general value of - satisfying tan-tan 3-4- -2 are

Consider the system of linear equations in x, y and z ;
(sin 3 $θ$ ) x - y + z = 0 ......(i)
(cos 2 $θ$ )x + 4y + 3z = 0 ......(ii)
2x + 7y+ 7z = 0 ......(iii)

The value of $θ$ for which the system has nontrivial solution is

Q. The general solution of

tan α + 2 tan 2 α + 4 tan 4 α + 8 cot 8 α = \sqrt{3}

(where n \in Z)

Join BYJU'S Learning Program

The most general value of θ satisfying tanθ+tan(3π4+θ)=2 are

The correct option is A nπ±π3,nϵZSimplifying it, tanθ+tanθ−1tanθ+1=2 tanθ(1+tanθ)+tanθ−1=2(1+tanθ) tan2θ=3 tanθ=√3=tanπ3 So, θ=nπ±π3

The most general value of $θ$ satisfying $tan θ + tan (\frac{3 π}{4} + θ) = 2$ are

The correct option is A $n π \pm \frac{π}{3}, n ϵ Z$
Simplifying it,
$tan θ + \frac{tan θ - 1}{tan θ + 1} = 2$

$tan θ (1 + tan θ) + tan θ - 1 = 2 (1 + tan θ)$

${tan}^{2} θ = 3$

$tan θ = \sqrt{3} = tan \frac{π}{3}$

So,
$θ = n π \pm \frac{π}{3}$