What is the maximum value of sin4 θ + cos4 θ ?
Answer & explanation
Correct answer: option 4
⇒ sin4 θ + cos4 θ
= ( sin2 θ + cos2 θ)² - 2sin2 θ cos2 θ
= 1 - 2sin2 θ cos2 θ
= 1 - \(\frac{1}{2}\) ( 2sin θ cos θ )2
= 1 - \(\frac{1}{2}\) ( sin 2θ )2
For maximum value of expression, \(\frac{1}{2}\) ( sin2 θ )2 should be minimum
i.e. only possible, when sin2 θ = 0
∴ maximum value is 1.