The greatest value of sin4θ + cos4θ is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 1.
sin4θ + cos4θ
= (sin2θ)2 + (cos2θ)2
= (sin2θ + cos2θ)2 - 2sin2θcos2θ
= 1 - 2sin2θcos2θ [∵ sin2θ + cos2θ = 1]
The maximum value of this expression occurs when 2sin2θcos2θ will be minimized.
If θ = 90° then, 2sin2θcos2θ = 2sin290°cos290° = 0
Maximum value = 1 - 2sin2θcos2θ = 1 - 0 = 1
Therefore, the greatest value of sin4θ + cos4θ is 1.