Question

If cota=5/12 evaluate 2sina-3cosa/4sina-9cosa

Answer 1

cot=cos/son
Cot(a)=cos(a) / sin(a)
Cos(a)=5
Sin(a)=12

2sina-3cosa / 4sina-9cosa
2(12)-3(5) / 4(12)-9(5)
24-15 / 48-45
9/3
3

Answer 2

3.

Explanation:

We have a triangle where opposite side = 12 , adjacent side = 5 and hypotenuse = √(12^2 + 5^2) = 13 (because cot a = adjacent/ opposite side).

So 2sina - 3cosa / 4sina - 9cosa

= (2 * 12/13 - 3 * 5/13) / ( 4 * 12/13 - 9 * 5/13)

= (24/13 - 15/13) / (48/13 - 45/13)

= 9/13 / 3/13

= 9/13 * 13/3

= 3.