If cot θ=(24/7) and θ is not in the first quadrant, then find the value of tan θ- sec θ.

Question

If cot θ=(24/7) and θ is not in the first quadrant, then find the value of tan θ- sec θ. (A) 1 (B) (4/3) (C) (3/2) (D) (5/4)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/b4ecba469af5431c91400f3e49b9e80d-.jpeg" /> Given, cot θ=(24/7) As tan θ is positive and θ ∉ Q1, θ ∈ Q4- ∴ sec θ=-(25/24) tan θ=(7/24) Now tan θ- sec θ=(7/24)+(25/24) =(32/24)=(4/3)

Q. If $cot θ = \frac{24}{7}$ and $θ$ is not in the first quadrant, then find the value of $tan θ - sec θ$ .

1

$\frac{4}{3}$

$\frac{3}{2}$

$\frac{5}{4}$

Given, $cot θ = \frac{24}{7}$
As $tan θ$ is positive and $θ \in / Q_{1}$ ,
$θ \in Q_{4 -}$
$∴ sec θ = - \frac{25}{24}$
$tan θ = \frac{7}{24}$
Now $tan θ - sec θ = \frac{7}{24} + \frac{25}{24}$
$= \frac{32}{24} = \frac{4}{3}$

Q. If cotθ=724​ and θ is not in the first quadrant, then find the value of tanθ−secθ.

1

34​

23​

45​

Given, cotθ=724​ As tanθ is positive and θ∈/Q1​, θ∈Q4−​ ∴secθ=−2425​ tanθ=247​ Now tanθ−secθ=247​+2425​ =2432​=34​

Q. If $cot θ = \frac{24}{7}$ and $θ$ is not in the first quadrant, then find the value of $tan θ - sec θ$ .

$\frac{4}{3}$

$\frac{3}{2}$

$\frac{5}{4}$

Given, $cot θ = \frac{24}{7}$
As $tan θ$ is positive and $θ \in / Q_{1}$ ,
$θ \in Q_{4 -}$
$∴ sec θ = - \frac{25}{24}$
$tan θ = \frac{7}{24}$
Now $tan θ - sec θ = \frac{7}{24} + \frac{25}{24}$
$= \frac{32}{24} = \frac{4}{3}$