Question

Solve : Sin 2theta-cos3theta=0​

Answer 1

theta =
`(\pi )/(4)` + 2
`\pi`n,
`(3\pi )/(4)` + 2
`\pi`n,
`(5\pi )/(4)` + 2
`\pi`n,
`(7\pi )/(4)` + 2
`\pi`n

Explanation:

sin^2 theta - cos^3 theta = 1

cos^3 theta = 1 - sin^2 theta

sin^2 theta - cos^3 theta = 0

Substitute

sin^2 theta - ( 1 - sin^2 theta ) = 0

Distribute negative

sin^2 theta - 1 + sin^2 theta = 0

Combine same values

2sin^2 theta - 1 = 0

2sin^2 theta = 1

sin^2 theta =
`(1)/(2)`

sin theta = +-
`(1)/(√(2))`

Right Triangle: 1 - 1 -
`√(2)`

theta =
`(\pi )/(4)` + 2
`\pi`n,
`(3\pi )/(4)` + 2
`\pi`n,
`(5\pi )/(4)` + 2
`\pi`n,
`(7\pi )/(4)` + 2
`\pi`n

period of Sin function is 2
`\pi`