The value of operatornamecosec(-1410)° is equal to

Question

The value of operatornamecosec(-1410)° is equal to (A) 1 (B) (1/2) (C) 2 (D) None of these

Tardigrade Admin · Accepted Answer

Since, we know that operatornamecosec(-θ) =- operatornamecosec θ ∴ operatornamecosec(-1410°) =- operatornamecosec(360 × 4-30)° =-(- operatornamecosec 30°) = operatornamecosec 30° [∵ operatornamecosec(2 n π-θ)=- operatornamecosec θ] =2

Q. The value of $cosec (- 1410)^{\circ}$ is equal to

1

$\frac{1}{2}$

2

None of these

Since, we know that
$cosec (- θ) = - cosec θ$
$∴ cosec (- 141 0^{\circ})$
$= - cosec (360 \times 4 - 30)^{\circ}$
$= - (- cosec 3 0^{\circ})$
$= cosec 3 0^{\circ}$
$[∵ cosec (2 nπ - θ) = - cosec θ]$
$= 2$

Q. The value of cosec(−1410)∘ is equal to

1

21​

2

None of these

Since, we know that cosec(−θ)=−cosecθ ∴cosec(−1410∘) =−cosec(360×4−30)∘ =−(−cosec30∘) =cosec30∘ [∵cosec(2nπ−θ)=−cosecθ] =2

Q. The value of $cosec (- 1410)^{\circ}$ is equal to

$\frac{1}{2}$

Since, we know that
$cosec (- θ) = - cosec θ$
$∴ cosec (- 141 0^{\circ})$
$= - cosec (360 \times 4 - 30)^{\circ}$
$= - (- cosec 3 0^{\circ})$
$= cosec 3 0^{\circ}$
$[∵ cosec (2 nπ - θ) = - cosec θ]$
$= 2$