Prove- sin2-4-x-sin2-4-x-1

LHS =sin^ 2 ( π #160; 4 x ) +sin^ 2 ( π #160; 4 +x ) =[ sin( π #160; 4 x ) #160; ] #160; ^ 2 +[ sin( π #160; 4 +x ) #160 ...

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General Solution of Trigonometric Equation

Prove: sin2...

Question

Prove:
${sin}^{2} (\frac{π}{4} - x) + {sin}^{2} (\frac{π}{4} + x) = 1$

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Solution

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{sin}^{2} (\frac{π}{4} - x) ({sin}^{2} (\frac{π}{4} + x) = 1

Prove that:

$c o s^{2} (\frac{π}{4} - θ) - s i n^{2} (\frac{π}{4} - θ) = s i n 2 θ$

{sin}^{2} \frac{π}{6} + {cos}^{2} \frac{π}{3} - {tan}^{2} \frac{π}{4} = - \frac{1}{2}

{sin}^{2} \frac{π}{6} + {cos}^{2} \frac{π}{3} - {tan}^{2} \frac{π}{4} = - \frac{1}{2}

Find the value of $s i n^{2} \frac{π}{8}$ + $s i n^{2} \frac{π}{4}$

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