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QUESTION
Q
The maximum value of Sin4θ + Cos4θ is ?
The maximum value of Sin4θ + Cos4θ is ?
A
1
B
2
C
3
D
1/3
E
3/2
A
1
B
2
C
3
D
1/3
E
3/2
Solution
Sin4θ + Cos4θ
= (Sin2θ + Cos2θ)2 − 2Sin2θCos2θ
= 1 −...
Sin4θ + Cos4θ
= (Sin2θ + Cos2θ)2 − 2Sin2θCos2θ
= 1 − [(2SinθCosθ)2]/2
= 1 − [(Sin2θ)2/]2
Sin22θ is always positive; hence the maximum value is obtained when sin22θ is equal to zero.
Hence, the maximum value is
= 1 − 0
= 1
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