Question

How do you solve `2sinxcosx=1` and find all solutions in the interval `0<=x<360`?

Answer 1

Solution: in interval, `0<=x<=360, x= pi/4 and x= (5pi)/4`

Explanation:

`2sinxcosx=1 or sin2x=1`. Since `sin2x=2sinxcosx` The interval `0<=x<=360 :. 0<=2x<=720`. We know `sin(pi/2)=1 ; sin(2pi+pi/2)=1 :. 2x=pi/2 or x=pi/4 and 2x = (5pi)/2 or x= (5pi)/4`[Ans]