Question

cos⁴π/24-sin⁴π/24 equals to

Answer 1

cos pie = -1
-1^4 = 1

sin pie = 0

so anserr2is 1/24

Answer 2

$= > {cos}^{4} \frac{\pi}{24} - {sin}^{4} \frac{\pi}{24} \\ \\ = > { ({cos}^{2} \frac{\pi}{24}) }^{2} - { ({sin}^{2} \frac{\pi}{24} ) }^{2} \\ \\ = > ( {cos}^{2} \frac{\pi}{24} - {sin}^{2} \frac{\pi}{24} )( {cos}^{2} \frac{\pi}{24} + {sin}^{2} \frac{\pi}{24} ) \\ \\ = > {cos}^{2} \frac{\pi}{24} - {sin}^{2} \frac{\pi}{24} \\ \\ = > cos(2 \times \frac{\pi}{24} ) \\ \\ = > cos \frac{\pi}{12} = cos15 \\ \\ = > cos15 = cos(45 - 30) \\ \\ = > cos(45 - 30) \\ \\ = > cos45.cos30 + sin45.sin30 \\ \\ = > 1 \times \frac{ \sqrt{3} }{2} + 1 \times \frac{1}{2} \\ \\ = > \frac{ \sqrt{3} + 1}{2}$
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