Question

if cosa +sina =√2sina show that sina - cosa =√2cosa​

Answer 1

Answer:

Step-by-step explanation:

cosa + sina = √2sina

cosa = √2sina - 1sina

cos a = (√2-1)sina

now subsitute this value in second equation

sina - {√2-1)sina} = √2{(√2-1)sina}

1-(√2-1)sina =( 2-√2)sina

2-√2= 2-√2

hence proved

Answer 2

$\huge\mathtt\pink{Answer}$

$\bf \: cosa +sina =√2sina$

$\bf \: cosa =√2sina \: - 1sina$

$\bf \: cosa =(√2 - 1) sina$

$\bf \: now \: subsitute \: this \: value \: in \: second \: equation$

$\bf \: \: sina \: -( √2 - 1) \: sina \: = √2(√2 - 1)sina$

$\bf \: 1 - (√2 - 1) \: sina \: = (2 - √2) \: sina$

$\bf \: 2 - √2 = 2 - √2$

$\bf \: \: hence \: proved$