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`2cos^2x + sinxcosx - sin^2x = 0`

To solve sầu for x, consider the above expression as a quadratic equation. Then, factor.

`(2cosx - sinx) ( cosx + sinx) = 0`

Set each factor to zero & solve sầu for x.

> `2cosx - sinx = 0`

Divide both sides by cos...


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`2cos^2x + sinxcosx - sin^2x = 0`

To solve sầu for x, consider the above expression as a quadratic equation. Then, factor.

`(2cosx - sinx) ( cosx + sinx) = 0`

Set each factor to lớn zero & solve sầu for x.

> `2cosx - sinx = 0`

Divide both sides by cos x.

`2 - (sinx)/(cosx) = 0`

 `tanx = 2`

cảnh báo that tangent function is positive sầu at quadrants I và III. So,

 `x = 63.43` & `243.43` degrees

The other factor is:

> `cos x + sinx = 0`

Divide both sides by cos x.

`1 + sinx/cosx = 0`

`1 + tanx = 0`

`tung x = -1`

Tangent function is negative sầu at quadrant II & IV. The values of angle x:

`x = 135` and `315` degrees

Hence, the general solution of `2cos^2x + sinxcosx-sin^2x` are:

`x_1 = 63.43 + 360k`degrees

`x_2 = 135 + 360k` degrees

`x_3 = 243.43 + 360k` degrees and

`x_4 = 315 +360k` degrees

 


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