Question

if cos^4x-sin^4x=2/3 then 2cos^2x -1=​

Answer 1

Answer:

${cos}^{4} x \: - \: {sin}^{4} x \: = \frac{2}{3} \\ by \: factorization \\ ( {cos}^{2} x \: - \: {sin}^{2} x ) \times ( {cos}^{2} x \: + \: {sin}^{2} x )\: = \frac{2}{3} \\ ( {cos}^{2} x \: - \: {sin}^{2} x ) \times 1\: = \frac{2}{3} \\ ( {cos}^{2} x \: - \: {sin}^{2} x ) = \frac{2}{3} \\ ( {cos}^{2} x \: - (1 - \: {cos}^{2} x )) = \frac{2}{3} \\ ( {cos}^{2} x \: - 1 + \: {cos}^{2} x ) = \frac{2}{3} \\ 2{cos}^{2} x \: - 1 = \frac{2}{3}$