Question

? i) is sin teeta-costeeta=0
then value of sin4teeta
+ cos4 teeta = 1/2​

Answer 1

Answer:

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

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