Question

Giải phương trình lượng giác: 1. Sin ²x - 1 = 0 2. 4 Sin ²x - 1 = 0 3. 1 - 2sinx.cosx = 0

Answer 1

`1)sin^2 x-1=0`

`<=>sin^2 x=1`

`<=>cos x=0`

`<=>x=\pi/2+k\pi`    `(k in ZZ)`

____________________________________

`2)4sin^2 x-1=0`

`<=>sin^2 x=1/4`

`<=>[1-cos 2x]/2=1/4`

`<=>1-cos 2x=1/2`

`<=>cos 2x=1/2`

`<=>2x=[+-\pi]/3+k2\pi`

`<=>x=[+-\pi]/6+k\pi`   `(k in ZZ)`

____________________________________

`3)1-2sin x cos x=0`

`<=>1-sin 2x=0`

`<=>sin 2x=1`

`<=>2x=\pi/2+k2\pi`

`<=>x=\pi/4+k\pi`    `(k in ZZ)`