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Given f(x) = sin² x + sin²(x + π/3) + cos x · cos(x + π/3) and g(5/4) = 1, determine the value of gof(x).

1. 1
2. 0
3. sin x
4. None of these

Correct answer: 1

Solution

f(x) = sin^2 x + sin^2(x+pi/3) + cos x cos(x+pi/3) simplifies to the constant 5/4 for all x. Hence gof(x) = g(f(x)) = g(5/4) = 1.

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