Question

find the value of sec-1560​

Answer 1

Answer:

-2

Step-by-step explanation:

sec(-1560°) = -2

Answer 2

Answer: -1/2

Mathematical Procedure:

We have the formula cos (180° + θ) = - cos θ

Now to find the value of 1560° , we we will make a repeated application of the above formula 8 times. If we do that, we get:

cos 1560° = cos (180° + 1380) = - cos 1380

- cos 1380° = -cos (180° + 1200) = -(- cos 1200°) = cos 1200

cos 1200° = cos (180° + 1020) = - cos 1020

-cos 1020° =-cos (180° + 840) = - (-cos 840°) = cos 840

cos 840° = cos (180° + 660) = - cos 660

- cos 660 = -cos (180° + 480) = - (-cos 480) = cos 480

cos 480 = cos (180° + 300) = - cos 300

- cos 300 = -cos (180° + 120) = - (-cos 120) = cos 120

We know from trigonometric table that

cos 120° = -cos 60° = -1/2

Hence cos 1560° = -1/2 (Proved)

We can get the same result by taking 360° instead of 180° as shown below. This will cut down the number of steps and hence labour.

cos 1560° = cos (360° +1200) = cos (180° +180° +1200) = - cos (180° +1200)= cos 1200

cos 1200° = cos (360° + 840) = cos (180° + 180° + 840) = -cos (180° + 840)= cos 840

cos 840° = cos (360° + 480) = cos (180° +180°+ 480) =- cos (180°+ 480) = cos 480

cos 480 = cos (360° + 120) =cos (180° +180° + 120) =-cos (180° + 120) = cos 120

Since it is known that cos 120° = -cos 60° = -1/2,

∴ cos 1560° = -1/2 (Proved)