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What is the value of sin(105deg) + cos(105deg)?

1. 1/sqrt(2)
2. sqrt(3)/2
3. 1/2
4. 0

Correct answer: 1/sqrt(2)

Solution

Writing sin(105deg) + cos(105deg) as sqrt(2)*sin(105deg + 45deg) = sqrt(2)*sin(150deg) gives sqrt(2)*(1/2) = 1/sqrt(2), which equals cos(45deg).

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