If p cos^2(x)+sin^2(x)=r,express cos^2(x) n terms of p and r only?

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Answer 1 · 2018-03-21T15:02:28

${cos}^{2} x = \frac{r - 1}{p - 1}$ $cos^2x=(r-1)/(p-1)$

Given:
$p {cos}^{2} x + {sin}^{2} x = r$ $pcos^2x+sin^2x=r$

${cos}^{2} x = f (p, r)$ $cos^2x=f(p,r)$

${sin}^{2} x = 1 - {cos}^{2} x$ $sin^2x=1-cos^2x$

$p {cos}^{2} x + 1 - {cos}^{2} x = r$ $pcos^2x+1-cos^2x=r$

$1 + (p - 1) {cos}^{2} x = r$ $1+(p-1)cos^2x=r$

$(p - 1) {cos}^{2} x = r - 1$ $(p-1)cos^2x=r-1$

${cos}^{2} x = \frac{r - 1}{p - 1}$ $cos^2x=(r-1)/(p-1)$