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Given tan(theta) = 2x(x+1)/(2x+1), find sin(theta) and cos(theta).

1. sin = (2x²+2x)/(2x²+2x+1), cos = (2x+1)/(2x²+2x+1)
2. sin = (2x+1)/(2x²+2x+1), cos = (2x²+2x)/(2x²+2x+1)
3. sin = (2x²+2x)/(2x²+2x-1), cos = (2x+1)/(2x²+2x-1)
4. sin = (2x+1)/(2x²+2x), cos = (2x²+2x)/(2x+1)

Correct answer: sin = (2x²+2x)/(2x²+2x+1), cos = (2x+1)/(2x²+2x+1)

Solution

With P = 2x²+2x and B = 2x+1, P² + B² = (2x²+2x+1)², so the hypotenuse is 2x²+2x+1, giving the stated sine and cosine.

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