Question

cos (2pi + theta) cosec ( 2 pi + theta ) tan ( pi/2 +theta ) / sec( pi/2 + theta ) cos theta cot ( pi + theta)

Answer 1

Please see the attachment

Answer 2

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/* We know that,

$cos(2\pi + \theta) = cos \theta \\cosec (2\pi + \theta) = Cosec \theta \\tan (\frac{\pi}{2}+ \theta)= -cot \theta \\</p><p>sec(\frac{\pi}{2} + \theta) = - Cosec \theta \\cot (\pi + \theta) = cot \theta$

_____________________ */

$Value \:of \: \frac{cos(2\pi + \theta)cosec (2\pi + \theta) tan (\frac{\pi}{2}+ \theta)}{ sec(\frac{\pi}{2} + \theta)cos \theta cot (\pi + \theta)}$

$= \frac{cos \theta Cosec \theta (-cot\theta) }{ (-cosec \theta ) cos \theta cot \theta } \\=\frac{-cos \theta Cosec \theta cot\theta }{- cosec \theta cos \theta cot \theta } \\= 1$

Therefore.,

$\red{ Value \:of \: \frac{cos(2\pi + \theta)cosec (2\pi + \theta) tan (\frac{\pi}{2}+ \theta)}{ sec(\frac{\pi}{2} + \theta)cos \theta cot (\pi + \theta)}}\green {= 1 }$

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