Question

If sin a- cos a = -√2 sin a then cos a + sin a = _____. ​

Answer 1

Answer:

cos a + sin a = 0.

Step-by-step explanation:

$sin \: a - cos \: a = - \sqrt{2}$

$squaring \: on \: both \: sides \\ = = > {(sin \: a - cos \: a)}^{2} = { - \sqrt{2} }^{2} \\ = = > {sin}^{2} a + {cos}^{2} a - 2sin \: a \: cos \: a = 2 \\ = = > 1 - 2 \: sin \: a \: cos \: a = 2 \: as \: {sin}^{2}a + {cos}^{2}a = 1 \\ = = > - 2 \: sin \: a \: cos \: a = 1 \\ = = > 2 \: sin \: a \: cos \: a = - 1$

$now \: take \: cos \: a + sin \: a = x \\ squaring \: on \: both \: side \\ {(cos \: a + sin \: a)}^{2} = {x}^{2} \\ {cos}^{2} a + {sin}^{2} a + 2 \: sin \: a \: cos \: a \: = {x}^{2} \\ 1 + 2 \: sin \: a \: cos \: a = {x}^{2} \\ 1 - 1 = {x}^{2} \: as \: 2 \: sin \: a \: cos \: a = - 1 \\ 0 = {x}^{2} \\ x = 0$