The most general value of θ, satisfying the two equations, cos θ = (1/√2) , tan θ = 1 is :

Question

The most general value of θ, satisfying the two equations, cos θ = (1/√2) , tan θ = 1 is : (A) 2 n π ± (5 π/4) (B) 2 n π ± (π/4) (C)  n π ± (5 π/4) (D) (2 n + 1) π + ( π/4)

Tardigrade Admin · Accepted Answer

The values of θ lying between 0 and 2 π and satisfying the given equations is θ = (5 π/4). Hence, the general value of θ satisfying the given equation is θ = 2 n π + (5 π/4) ⇒ θ = (2 n + 1) π + (π/4)

Q. The most general value of $θ$ , satisfying the two equations, $cos θ = \frac{1}{2}, tan θ = 1$ is :

$2 nπ \pm \frac{5 π}{4}$

$2 nπ \pm \frac{π}{4}$

$nπ \pm \frac{5 π}{4}$

$(2 n + 1) π + \frac{π}{4}$

The values of $θ$ lying between 0 and $2 π$ and satisfying the given equations is $θ = \frac{5 π}{4}$ .
Hence, the general value of $θ$ satisfying the given equation is
$θ = 2 nπ + \frac{5 π}{4} \Rightarrow θ = (2 n + 1) π + \frac{π}{4}$

Q. The most general value of θ, satisfying the two equations, cosθ=2​1​,tanθ=1 is :

2nπ±45π​

2nπ±4π​

nπ±45π​

(2n+1)π+4π​