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math Verify if sin15=(6^1/2-2^1/2)/4.

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To show that sin 15 = (6^1/2 - 2^1/2)/4, let's start with the values of the functions of a number that is well known, sin 30 = 1/2 and cos 30 = (sqrt...

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giorgiana1976 | Student

We'll notice that 15 is the half of 30 degrees.

We'll write the half angle identity:

sin (a/2) = sqrt [(1-cos a)/2]

We'll put a = 30 and we'll get;

sin (30/2) = sqrt [(1-cos 30)/2]

We'll substitute cos 30 = sqrt3/2

sin 15 =  sqrt [(1- sqrt3/2)/2]

sin 15 =  sqrt [(2- sqrt3)/4]

sin 15 =  sqrt(2- sqrt3)/2

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