Question

Sin theta minus cos theta is equal to 0 find the value of sin race 4 theta plus cos race to 4 theta

Answer 1

Answer:

1/2

Step-by-step explanation:

sin theta -cos theta =0

implies sin theta =-cos theta

we know sin theta =-cos theta at theta = 45degrees

where both are equal to 1/root2

now sin theta raised to 4 =1/4=-cos theta raised to 4

therefore answer is 1/4+1/4=1/2

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