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Answer 1

Answer:

$tan( \pi \: cos \theta) = cot( \pi \: sin \theta) \\ \therefore \: tan( \pi \: cos \theta) = tan \: \{90 \degree - ( \pi \: sin \theta) \} \\\therefore \pi \: cos \theta=90 \degree - \pi \: sin \theta</p><p>\\\therefore \pi \: sin \theta+\pi \: cos \theta=90 \degree \\</p><p>\pi(sin \theta + cos \theta) =90\degree\\</p><p> Squaring \: both \:sides \\</p><p>\pi^2(sin \theta+cos \theta) ^2 =(90\degree)^2 \\</p><p>\pi^2( sin^2 \theta+cos^2 \theta + 2sin \theta cos\theta)=8100\degree\\</p><p>\pi^2( 1+sin 2\theta)=8100\degree\\</p><p>(1+sin 2\theta)=\frac {8100\degree} {\pi^2} \\</p><p>sin 2\theta=\frac {8100 \degree} {\pi^2}-1$