Find the value of cos 15 using cos (A-B) identity

We have to find the valye of cos 15 using cos (A-B) identity

Cos 15 we can write it as

Cos15 = Cos(45–30)…………………..(1)

By applying the formula

Cos (A – B) = Cos A. Cos B + Sin A. Sin B

Cos (45 – 30) = Cos 45. Cos 30 + Sin 45. Sin 30…………………..(2)

Sin Values

sin 0° = √(0/4) = 0

sin 30° = √(1/4) = ½

sin 45° = √(2/4) = 1/√2

sin 60° = √3/4 = √3/2

cos 90° = √(4/4) = 1

Cos Values

cos 0° = √(4/4) = 1

cos 30° = √(3/4) = √3/2

cos 45° = √(2/4) = 1/√2

cos 60° = √(1/4) = 1/2

cos 90° = √(0/4) = 0

Substitute the value of sin 30, sin 45, cos 30 and cos 45 degrees, then equation (2) will becomes

Cos (45 – 30) = 1/√2 . √3/2 + 1/√2 . 1/2

Cos 15 = √3/2√2 + 1/2√2

Cos 15 = √3+1/2√2

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