Question

If A = 30 show that
cos^3 A - cos 3A/ cos A + sin^3 A + sin 3A/sin A = 3

Answer 1

$Given\: A = 30 \degree \: --(1)$

$Value \: of \: \frac{cos^{3}A-cos A}{cos A } + \frac{sin^{3}A-sin A}{sin A } \\= \frac{cos 3A}{cos A} + \frac{sin 3A}{sin A} \\= \frac{cos (3\times 30)}{cos 30) } + \frac{sin (3\times 30)}{cos 30) } \\= \frac{cos 90\degree}{cos 30} + \frac{sin 90\degree}{sin 30} \\= \frac{ 0}{\frac{\sqrt{3}}{2}} + \frac{1}{\frac{1}{2}} \\= 2$

Therefore.,

$\red { Value \: of \: \frac{cos^{3}A-cos A}{cos A } + \frac{sin^{3}A-sin A}{sin A }} \green {= 2}$

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