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Question

The value of cos(12cos1[cos(14π5)])

A
cos(9π5)
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B
sin(π5)
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C
cos(2π5)
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D
cos(3π5)
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Solution

The correct option is C cos(2π5)
Let be very careful about the interval in which the angle belongs to.
θ=14π5=2.8π
3π < θ < 2π
i.e.,[2(-1)-1] π < θ < 2π.
cos1(cosθ)=2(1)πθ=2πθ=2π+14π5=4π5cos(12cos1.cos(14π5))=cos(12.4π5)=cos(2π5)

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