Cos105º-sin195º+sin(-135º)

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To find the value of this expression, we need to first convert the angles to their equivalent acute angles within the unit circle.

105º is equivalent to 105º - 360º = -255º. Since -255º is in the fourth quadrant, the reference angle would be 255º.

195º is equivalent to 195º - 180º = 15º. Since 15º is in the first quadrant, the reference angle remains 15º.

-135º is equivalent to -135º + 360º = 225º. Since 225º is in the third quadrant, the reference angle would be 225º.

Now we can find the sine and cosine values for the reference angles:

cos(255º) = -cos(75º) = -√3/2
sin(15º) = sin(15º) = 1/2
sin(225º) = -sin(45º) = -√2/2

Now we can substitute these values back into the expression:

cos(105º) - sin(195º) + sin(-135º)
= -√3/2 - 1/2 + (-√2/2)
= -√3/2 - 1/2 - √2/2
= -√3/2 - √2/2 - 1/2

Therefore, the value of the expression is -√3/2 - √2/2 - 1/2.