Question

If 2sin theta =2-cos theta and 0°<theta<90°. Find sin theta​

Answer 1

Answer:

sin theta = 1 or 3/5

Step-by-step explanation:

2sin theta =2-cos theta

from identity sin²theta + cos²theta =1

therefore cos²theta =1-sin²theta

square root both sides we get cos theta =√1-cos² theta

therefore 2sin theta = 2 - √1-sin² theta

√1-sin² theta=2-2sin theta

square both sides we get

1-sin² theta = (2-2sin theta)²

1-sin² theta = 4 - 8sin theta + 4sin² they

so 5sin² theta - 8 sin theta + 3 =0

5sin² theta - 3sin theta -5sin theta +3 =0

sin theta(5sin theta - 3) -1(5sin theta -3) =0

(sin theta - 1)(5sin theta - 3)=0

sin theta -1=0 or 5sin theta - 3=0

so sin theta = 1 or sin theta = 3/5

I hope this helps