Explain two methods to elucidate the value of cos 45 using sin x and cos x

We need to find the value of cos 45

Solution

We can find using two methods

Method 1

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

We know that cot x = 1/tan x

So cot 45° = 1/Tan 45°

cot 45°=1/1=1

Hence cot 45°=1

Method 2

We have learnt that

cos α = 1 / tan α = 1 / sin α / cos α= cos α / sin α

So, cos 45 degrees can be represented as

cos 45°=cos 45°/ sin 45°

We know that

Sin 45° = 1/√2 & Cos 45° = 1/√2 ∴

cos 45° = (1/√2) /(1/√2)

cos 45° = 1

Answer

Hence cos 45° = 1

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