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Product of Trigonometric Ratios in Terms of Their Sum

Evaluate: si...

Question

Evaluate:
${sin}^{2} 0 + {sin}^{2} {(\frac{π}{6})}^{c} + {sin}^{2} {(\frac{π}{3})}^{c} + {sin}^{2} {(\frac{π}{2})}^{c}$ ?

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Solution

$= {(sin 0)}^{2} + (sin 30)^{2} + (sin 60)^{2} + (sin 90)$
$= 0 + {(\frac{1}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2} + 1$
$= 2$

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Product of Trigonometric Ratios in Terms of Their Sum

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