Question

evaluate sin^2 42°-sin^212°
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Answer 1

$answer : - \\ \\ {sin}^{2} 42 - {sin}^{2} 12 \\ \\ \sf \implies \: sin \: (42 - 12) \: sin(42 - 12) \\\sf \implies \: sin \: 54.sin \: 30 \\ \sf \implies \: sin \: (90 - 36) \times \frac{1}{2} \\ \sf \implies \: cos \: 36 \times \frac{1}{2} \\ \sf \implies \: \frac{ \sqrt{5} + 1}{4} \times \frac{1}{2} \\ \sf \implies \: \frac{ \sqrt{5} + 1 }{8}$