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Question

The value of cot2212is equal to


A

1+12

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B

1+2

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C

2-1

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D

None of these

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Solution

The correct option is B

1+2


Explanation for the correct option:

Find the required value

Given: cot2212

Let θ=45
Andθ2=452=2212
As we know that cotx=cosxsinx
So, cotθ2=cosθ2sinθ2
And we can write it as,
cotθ2=[2cosθ2cosθ2][2sinθ2cosθ2]

cotθ2=2cos2θ22sinθ2cosθ2

cotθ2=1+cosθsinθ [sin2θ=2sinθcosθand cos2θ=2cos2θ1]
Now, substituting the values of θ and θ2 , we get,
cot2212=(1+cos45)sin45=1+1212=2+1212=1+2

Therefore, the value of is cot2212equal to 1+2.

Hence, option (B), 1+2 is the correct answer.


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