Evaluate sin78 – sin66 – sin42 + sin6.

Solution :

The expression = (sin78 – sin42) – (sin66 – sin6)

= 2cos(60)sin(18) – 2cos36.sin30

= sin18 – cos36

= \(({\sqrt{5} – 1\over 4})\) – \(({\sqrt{5} + 1\over 4})\) = -\(1\over 2\)


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