Question

if 5 tan=4 then, 5 sin -3cos÷ sin +2 cos​

Answer 1

Answer:

Step-by-step explanation:

Given that,

5 tan x = 4

tan x = 4/5 = AB / BC ( ∵ let ΔABC is a right angle triangle )

We find AC,

By using Pythagoras theorem

AC² = AB² + BC²

AC² = 4² + 5²

AC² = 16 + 25

AC² = 41

AC = √ 41

∴ 5 sin x - 3 cos x ÷ sin x + 2 cos x

= 5 ( AB / AC ) - 3 ( BC /AC ) ÷ ( AB / AC ) + 2 ( BC / AC )

= 5 × 4/√41 - 3 × 5/√41 ÷ 4/∛41 + 2 × 5/√41

= 20 / √41 - 15 / √41 ÷ 4/√41 + 10 / √41

= ( 20 - 15 ) / √41 ÷ ( 4 + 10 )/ √41

= 5 / √41 ÷ 14 / √41

= 5 / √41 × √41 / 14

= 5 / 14 is the answer.