Find the exact value of the expression. cos(160[])cos(40[])+sin(160[])sin(40)?

Question: 1. -sqrt[]3 2.-1/2 3. -sqrt[]3/2 4. -2

Answer: It looks like you made a typo. I'm guessing that the real question is an expansion of cos (160 degrees - 40 degrees). I.e., it's cos (120 degrees). That said, one of the basic things you learn in trig is how to quickly calculate any of the six trig functions of any angle that's a multiple of 30 degrees (also known as pi/6 radians) or of 45 degrees (also known as pi/4 radians). For example, cos(t) = -cos (180 degrees - t), for any t. So cos (120 degrees) = -cos (60 degrees). And you'd better know what cos(60 degrees) is. :)

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