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Reduction Formulae

Prove that: ...

Question

Prove that:
$2 s i n^{2} \frac{3 π}{4} + 2 c o s^{2} \frac{π}{4} + 2 s e c^{2} \frac{π}{3} = 10$

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Solution

$L H S = 2 s i n^{2} \frac{3 π}{4} + 2 c o s^{2} \frac{π}{4} + 2 s e c^{2} \frac{π}{3}$
$= 2 {sin}^{2} (π - \frac{π}{4}) + 2 {(\frac{1}{\sqrt{2}})}^{2} + 2 {(2)}^{2} = 2 {(\frac{1}{\sqrt{2}})}^{2} + 1 + 8 = 10 = R H S$

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