Question

. If lies in the first quadrant and 5 tan 0 = 4, then
5 sin 0 - 3 cos 0/
sin 0 + 2 cos 0
1) 5/14 2) 3/14 3) 1/14 4)​

Answer 1

Answer:

1)5/14

Step-by-step explanation:

tan 0= 4/5

1. 1+ tan²0 = sec 0

2. sec 0 = √1+ (4/5)²

= √1+ 16/√25

= √25 +16/√25

= √41/√25

sec0 = √41/ 5

3. cos 0= 5/√41

4. tan 0* cos 0= sin 0

4/5 * 5/√41 = sin 0

sin 0= 4/√41

5. 5sin 0 - 3cos 0/

sin 0 + 2cos 0

=5*4/√41 - 3*5/√41 /

4/√41 + 2*5/√41

=20/√41 - 15/√41 /

4/√41 + 10/√41

=20-15/√41 /

14/√41

=5/√41 /

14/√41

=5/14.