Question

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

Answer 1

Answer:

Hope It will help you.....☺

Answer 2

Step-by-step explanation:

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