# What is the value of sum of sqrt2/2+sinx=?

Rylan Hills | Certified Educator

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This is a weird question, it is not possible to determine "the value of sum of sqrt2/2+sinx=?" as sin x is a variable.

I guess you want the...

(The entire section contains 80 words.)

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giorgiana1976 | Student

To determine the value of the sum, we'll create matching functions in the given sum.

Since sin pi/4 = (sqrt2)/2, we'll substitute the value (sqrt2)/2 by the equivalent function of the angle pi/4.

We'll transform the sum  into a product.

sin x + sin pi/4 = sin x + (sqrt2)/2

sin x + sin pi/4  =  2sin [(x+pi/4)/2]*cos[ (x-pi/4)/2]

sin x + sin pi/4  = 2 sin [(x/2 + pi/8)]*cos[ (x/2 - pi/8)]

We'll use the half angle identity:

sin [(x+pi/4)/2] = sqrt[2-(sqrt2)*(cos x-sin x)]/2

cos[ (x-pi/4)/2] = sqrt[2+(sqrt2)*(cos x+sin x)]/2

sin x + sin pi/4  = sqrt{[2-(sqrt2)*(cos x-sin x)]*[2+(sqrt2)*(cos x+sin x)]}/2

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