Question

(sin^4 a - cos^4 a + cos^2 a)/ 2(1-cos a)

Answer 1

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Answer 2

$\displaystyle \frac{\sin^4 \alpha-\cos^4 \alpha+\cos^2 \alpha }{2(1-\cos \alpha)} = \frac{(\sin^2 \alpha+\cos^2 \alpha)(\sin^2 \alpha-\cos^2 \alpha)+\cos^2 \alpha}{2(1-\cos \alpha)} =\\ \\ \\ = \frac{\sin^2 \alpha-\cos^2 \alpha+\cos^2 \alpha}{2(1-\cos \alpha)} = \frac{\sin^2\alpha}{2(1-\cos \alpha)}= \frac{1-\cos^2\alpha}{2(1-\cos \alpha)} \\ \\ =\frac{(1-\cos \alpha)(1+\cos \alpha)}{2(1-\cos \alpha)} = \frac{1+\cos \alpha }{2} =\cos^2 \frac{ \alpha}{2}$