Question

If 3 tan theta = 4, find the value of

5 sin theta - 3 cos theta /
5 sin theta + 2 cos theta​

Answer 1

Answer:

11/26

Step-by-step explanation:

3 tanX = 4

tanX = sinX / cosX

• 3( sinX / cosX ) = 4
• 3 sinX = 4 cosX ------------------ eq.1

(5 sinX - 3 cosX ) / ( 5 sinX + 2 cosX ) =?

Substituting eq.1,

1. (5(4/3 cosX) - 3cosX) / (5(4/3 cosX) + 2cosX)
2. (20/3 cosX - 3 cosX)/( 20/3 cosX + 2cosX)
3. (11/3 cosX) / (26/3 cosX)
4. 11/26