Question

please solve this equation​

Answer 1

Answer:

answers are given for the given problem

Answer 2

Answer:

given: 3 cot x = 4

to evaluate (5 sin x - 3 cos x)/(5 sin x + 3 cos x)

3 cot x = 4 => cot x = 4/3

=> cot x = base/perpendicular

=> therefore, base = 4 and perpendicular = 3

and by Pythagoras theorem, hypotenuse = 5

now, sin x = perpendicular/hypotenuse

=> sin x = 3/5

cos x = base/perpendicular

=> cos x = 4/5

substitute these values in the given expression,

=> (5 * 3/5 - 3*4/5)/(5*3/5 + 3*4/5)

=> (3 - 12/5)/(3 + 13/5)

=> [(15 - 12)/5] / [(15 + 12)/5]

=> (3/5)/(27/5)

=> 3/27

=> 1/9 Answer

if 5 cos x - 12 sin x = 0

evaluate (sin x + cos x)/(2 cos x - sin x)

=> 5 cos x - 12 sin x = 0

=> 5 cos x = 12 sin x

=> 5/12 = sin x/cos x= tan x [by transposing]

=> tan x = 5/12 => perpendicular/base

=> perpendicular = 5 base = 12

therefore by Pythagoras theorem, hypotenuse= 13

therefore sin x = 5/13 cos x = 12/13

substitute these values in the given expression,

(5/13 + 12/13) / ( 2*12/13 - 5/13)

=> (17/13)/(19/13)

=> 17/19