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Evaluate: (a) sin(pi/10) + sin(13*pi/10) and (b) cos²(48 deg) - sin²(12 deg). Which option gives the correct pair of values?

1. (a) -1/2, (b) (sqrt(5)+1)/8
2. (a) 0, (b) 1/2
3. (a) 1, (b) (sqrt(5)-1)/4
4. (a) -1, (b) 1/4

Correct answer: (a) -1/2, (b) (sqrt(5)+1)/8

Solution

(a) sin18 + sin234 = sin18 - sin54 = (sqrt5-1)/4 - (sqrt5+1)/4 = -1/2; (b) cos² 48 - sin² 12 = cos60 cos36 = (1/2)((sqrt5+1)/4) = (sqrt5+1)/8.

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