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Question

If sin(πcotθ4)=cos(πcotθ4) and θ is in the first quadrant, then θ =

A
π/3
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B
π/2
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C
π/4
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D
None of these.
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Solution

The correct option is C π/4
Given,

sin(πcotθ4)=cos(πcotθ4)

sin(πcotθ4)=sin(π2πcotθ4)

πcotθ4=π2πcotθ4

2πcotθ4=π2

cotθ=1

θ=cot1(1)=π4


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