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How do you use the sum or difference identities to find the exact value of #cos105^circ#?

Answer 1

#- (sqrt(2 - sqrt3))/2#

Use trig identity: #2cos^2 a = 1 + cos 2a# #2cos^2 (105) = 1 + cos (210)#. Find cos (210) Use trig table and unit circle #cos (210) = cos (30 + 180) = - cos 30 = - sqrt3/2# #2cos^2 (105) = 1 - sqrt3/2 = (2 - sqrt3)/2# #cos^2 (105) = (2 - sqrt3)/4# #cos (105) = +- sqrt(2 - sqrt3)/2# Since cos 105 (Quadrant II) is negative, take the negative value as answer.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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