Find the value of sin75°

Answer: (√3 + 1)/ 2√2

Sin 75 we can write it as

Sin 75 = Sin(45+30)…………………..(1)

By applying the formula

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

Sin (45 + 30) = Sin 45. Cos 30 + Cos 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

Sin (45 + 30) = Sin 45. Cos 30 + Cos 45. Sin 30

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

Sin (45 + 30) = (√3 + 1) / 2√2

Hence the value of Sin 75 degree is equal to (√3 + 1) / 2√2.

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