Question

If sin theta-cos theta=0,then find the value of sin ^4 theta+cos^4 theta

Answer 1

$Hey\:There$‼

Given that, sin θ – cos θ = 0

sin θ = cos θ 

sin θ / cos θ = tan θ 

=> tan 45° = 1

=> θ = 45°

Now,
sin⁴ θ + cos⁴ θ 

= ( sin² θ )² + ( cos² θ )²

= ( sin² 45° )² + ( cos² 45° )²

= [ ( 1 / √2 )² ]² + [ ( 1 / √2 )² ]²

= ( 1 / 2 )² + ( 1 / 2 )²

= ( 1 / 4 ) + ( 1 / 4 )

= ( 1 + 1 ) / 4

= 2 / 4

= 1 / 2

Answer 2

Answer:

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