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Evaluate and verify the identity: is sin75 deg - sin15 deg equal to cos105 deg + cos15 deg? State the common value.

1. Yes, both equal 1/sqrt(2)
2. No, they are not equal
3. Yes, both equal sqrt(3)/2
4. Yes, both equal 1/2

Correct answer: Yes, both equal 1/sqrt(2)

Solution

sin75 - sin15 = 2 cos45 sin30 = 2*(1/sqrt2)*(1/2) = 1/sqrt2, and cos105 + cos15 = 2 cos60 cos45 = 2*(1/2)*(1/sqrt2) = 1/sqrt2, so both sides equal 1/sqrt2.

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