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Question

If (tan1x)2+(cot1x)2=5π28, then the value of x is

A
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B
1
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Solution

The correct option is B 1
(tan1x)2+(cot1x)2=5π28
(tan1x+cot1x)22tan1xcot1x=5π28
π242tan1xcot1x=5π28
tan1xcot1x=3π216 (1)
Lettan1x=t
Then, equation (1) becomes
t(π2t)=3π216
t=π4,3π4
x=tant=1

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