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Why is sin (x+y) not equal to sin x + sin y ???

Sine of an angle is the ratio of perpendicular and the hypotenuse of the triangle.

So, sin(x+y) is is the ratio of sum of two angles
Whereas, sinx + siny is the sum of two ratios

For example:

sin(30°+60°)= sin90° =1

Whereas,

sin30° +sin60°= 12+32=1+1.7322=2.7322which is not same as sin(30°+60°)

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Simply because sin is a dynamic variable. In case of 1,2,3,4 , the above would be possible.

Sin depends on the angle

For Eg:

sin ( 30 + 60) = sin 90

sin 90 = 1

sin 30 = 1/2

sin 60 = root 3/2

Clearly sin 30 + sin 60 is not = 1

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