Question

sin^3 x cos x+cos^3 x sin x= sin x cos x​

Answer 1

Answer:

${sin}^{3} x \: cosx \: + {cos}^{3} x \: sinx \\ = sinx \: cosx \: ( {sin}^{2} x \: + {cos}^{2} x) \\ = sinx \: cosx \: (1) \\ = sinx \: cosx$

Answer 2

Step-by-step explanation:

${sin}^{3} x\: \: cosx \: + {cos}^{3}x \: \: sinx \: = sinx \: cosx$

$LHS \: = \: sin \: x \: \: cos \: x( {sin}^{2} \: x + c {os}^{2} \: x)$

we know that,

${sin \: }^{2} \: x \: + {cos}^{2} \: x = 1$

now,

$= sin \: x \: \: cos \: x \: (1)$

$= sin \: x \: \: cos \: x$