Question

if tan theeta = 4,show that
(4cos theeta-sin theeta)
(2costheeta+sin theeta)
​

Answer 1

Answer:

Step-by-step explanation:

If 3 tan  ϴ = 4

tan  ϴ = 4/3

Now  4 cos  ϴ - sin  ϴ/ 2 cos  ϴ + sin ϴ

= {4 cos  ϴ - sin ϴ / cos  ϴ} / 2 cos  ϴ + sin  ϴ/ cos  ϴ

= 4 cos  ϴ/cos  ϴ - sin  ϴ / cos  ϴ} 2 cos  ϴ /cos  ϴ + sin  ϴ /cos  ϴ

= 4 - tan ϴ / 2 + tan  ϴ

= {4 - 4/3 }/2+ 4/3

= 8 /3 /10/3

= 8/10

= 4/5,

Hence proved.