Question

If cosec A = 13÷12, find the value of 3cotA - 2tan A ​

Answer 1

-71÷20 or -3.55

Explanation:

cosec A = 1/sin A

13/12 = 1/sin A

sin A = 12/13

Since we know that sin A formula is derived from:

sin A = opposite/hypotenuse

if Opposite is 12, hypotenuse is 13, then adjacent is:

Adjacent² = Hypotenuse² - Opposite²

Adjacent² = 13² - 12²

Adjacent² = 169 - 144

Adjacent² = 25

Adjacent² = 5²

Adjacent = 5

cos A = adjacent/hypotenuse

cos A = 5/13

Rule:

cot A = 1/tanA = cos A/sin A

cot A = 1/tanA = cos A/sin Atan A = sin A/cos A

Find The Value by Inputting sin A & cos A value

3cot A - 2tan A:

= 3 (cos A/sin A) - 2 (sin A/cosA)

= 3 (5/13 / 12/13) - 2 (12/13 / 5/13)

= 3 (5/12) - 2 (12/5)

= 5/4 - 24/5

= 25/20 - 96/20

= -71/20 or -3.55

Hope it helps. Thanks!