How do you find the value of cot 45°?

We have learnt that

Tan α = sin α/cos α

So, tan 45 degrees can be represented as

Tan 45°=sin 45°/cos 45°

We know that

Sin 45° = 1/√2 & Cos 45° = 1/√2

Tan 45° = (1/√2) /(1/√2)

Tan 45° = 1

cot 45°= 1 / tan 45° = 1/1=1

Alternative method

We know that

cot x = cos x / sin x

cot 45 = cos 45 / sin 45

Hence

Sin 45° = 1/√2 & Cos 45° = 1/√2 ∴

cot 45 = 1/√2 / 1/√2

cot 45 = 1

Answer

cot 45 = 1

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