Discussion

Explanation:

0 < θ < π/4, let's take θ = 30°

sin30° = 1/2 = 0.5, cos30° = √3/2 = 0.866

a = ((sinθ)^sinθ)(log₂cosθ), 
⇒ a = ((1/2)^1/2)(log₂0.866) 

b = ((cosθ)^sinθ)(log₂sinθ), 
⇒ b = ((0.866)^1/2)(log₂1/2), 

c = ((sinθ)^cosθ)(log₂cosθ) 
⇒ c = ((1/2)^0.866)(log₂0.866) 

d = ((sinθ)^sinθ)(log₂sinθ)
⇒ d = ((1/2)^1/2)(log₂1/2)

(1/2)^0.5 > (1/2)^0.866 ​​​​​​​and (log₂0.866) is negative
∴ c is greater than a.

Similarly, c > a > d > b.

∴ Median of these four numbers = average of 2 middle numbers = (a + d)/2

Hence, option (b).

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