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Question

State whether the given statement is true or false
1+cotθcotθ/2 for 0<θ<π. Find θ when equality signs holds.If this is true enter 1, else enter 0.

A
True
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B
False
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Solution

The correct option is B False
Given, 1+cosθsinθcosθ2sinθ2
sinθ+cosθsinθcosθ2sinθ2
sinθ+cosθ2sinθ2.cosθ2cosθ2sinθ2
sinθ+cosθ2sinθ2.cosθ22cos2θ22sinθ2.cosθ20
1sinθ[sinθ+cosθ(1+cosθ)]0
cosecθ[sinθ1]0
1cosecθ0
1cosecθ
sinθ1
sinθ=1 or sinθ>1
But, |sinθ|1
Hence, sinθ=1
θ=π2.

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