Prove the following- sin2-4-xsin2-4-x-1

sin^2(π4 x)(sin^2(π4+x)=1 =2(sin^2π4cos^2x+cos^2π4sin^2x) =2(cos^2x+sin^2x2) =1 ...

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Use of Trigonometric Table

Prove the fol...

Question

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

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

{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}

Prove that:

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

s i n^{2} (\frac{π}{8} + \frac{A}{2}) - s i n^{2} (\frac{π}{8} - \frac{A}{2}) = \frac{1}{\sqrt{2}} s i n A

c o s^{2} 45^{o} - s i n^{2} 15^{o}

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