Question

if sinx+cosx=0, then find the value of sin^4x+cos^4x​

Answer 1

$HEYA \:$

Sin⁴x + Cos⁴x =

( Sin²x + Cos²x )² - 2 ( Sinx × Cos x )²

Becoz ( a⁴ + b⁴ ) = ( a² + b² )² - 2( ab )²

Sin⁴x + Cos⁴x =

1² - 2 Sin²x × Cos²x

Becoz ( Sin²x + Cos²x ) = 1

Sin⁴x + Cos⁴x =

1 - 2 Sin²x ( 1 - Sin²x )

Sin⁴x + Cos⁴x =

1 - 2Sin²x + 2 Sin⁴x

OR

Sin⁴x + Cos⁴x =

1 - 2 Cos²x + 2 Cos⁴x