Question

If cos titha -sin titha=√2sin titha Prove that cos titha +sin titha =√2cos titha​

Answer 1

Step-by-step explanation:

$cos \alpha - sin \alpha = \sqrt{2} sin \alpha \\ squaring \: on \: both \: sides \\ {cos}^{2} \alpha + {sin}^{2} \alpha \: - 2sin \alpha \: cos \alpha = 2 {sin}^{2} \alpha \\ 1 - {sin}^{2} \alpha + 1 - {cos}^{2} \alpha - 2sin \alpha \: cos \alpha = 2 {sin}^{2} \alpha \\ {sin}^{2} \alpha + {cos}^{2} \alpha + 2sin \alpha \: cos \alpha = 2(1 - {sin}^{2} \alpha ) \\ ( {sin \alpha + cos \alpha )}^{2} = 2 {cos}^{2} \alpha \\ sin \alpha + cos \alpha = \sqrt{2} cos \alpha \\ \\ hope \: it \: will \: help \: you..$