How do you solve $3 {sin}^{2} x - sin x cos x - 4 {cos}^{2} x = 0$ $3sin^(2)x - sinxcosx - 4cos^(2)x = 0$ from [-pi, pi]?

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How do you solve $3 {sin}^{2} x - sin x cos x - 4 {cos}^{2} x = 0$ $3sin^(2)x - sinxcosx - 4cos^(2)x = 0$ from [-pi, pi]?

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Answer 1 · 2015-09-07T13:41:11

3 $y^{2}$ $y^2$ - y $\sqrt{}$ $sqrt$ (1 - $y^{2}$ $y^2$ ) - 4 (1 - $y^{2}$ $y^2$ ) = 0, y = sinx
$\Rightarrow$ $=>$ 7 $y^{2}$ $y^2$ = y $\sqrt{}$ $sqrt$ (1 - $y^{2}$ $y^2$ ) $\Rightarrow$ $=>$ 7y = $\sqrt{}$ $sqrt$ (1 - $y^{2}$ $y^2$ )
$\Rightarrow$ $=>$ y = 1/5 $\sqrt{}$ $sqrt$ 2 $\Rightarrow$ $=>$ x = ${sin}^{- 1}$ $sin^- 1$ (1/ 5 $\sqrt{}$ $sqrt$ 2 )

Explanation:

Squaring 7y = $\sqrt{}$ $sqrt$ (1 - $y^{2}$ $y^2$ ), we get 49 $y^{2}$ $y^2$ = 1 - $y^{2}$ $y^2$ $\Rightarrow$ $=>$
50 $y^{2}$ $y^2$ = 1 $\Rightarrow$ $=>$ $y^{2}$ $y^2$ = 1/50 $\Rightarrow$ $=>$ y = 1/5 $\sqrt{}$ $sqrt$ 2 .

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How do you solve $3 {sin}^{2} x - sin x cos x - 4 {cos}^{2} x = 0$ $3sin^(2)x - sinxcosx - 4cos^(2)x = 0$ from [-pi, pi]?

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How do you solve $3 {sin}^{2} x - sin x cos x - 4 {cos}^{2} x = 0$ $3sin^(2)x - sinxcosx - 4cos^(2)x = 0$ from [-pi, pi]?