Question

14. দেখাও যে, (cos⁴x/2-sin⁴x/2) = cos x

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Answer 1

Answer:

$\cos {}^{4} ( \frac{x}{2} ) - \sin { }^{4} ( \frac{x}{2} ) \\ \\ =( \cos {}^{2} ( \frac{x}{2} ) ) {}^{2} - (\sin { }^{2} ( \frac{x}{2} ) ) {}^{2} \\ \\ = (\cos {}^{2} ( \frac{x}{2} ) - \sin { }^{2} ( \frac{x}{2} ) )(\cos {}^{2} ( \frac{x}{2} ) + \sin { }^{2} ( \frac{x}{2} ) ) \\ \\ = \cos {}^{2} ( \frac{x}{2} ) - \sin { }^{2} ( \frac{x}{2} ) \\ \\ = \cos(2x)$