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

$\frac{\cos (2 π + θ) \cos e c (2 π + θ) \tan (\frac{π}{2} + θ)}{\sec (\frac{π}{2} + θ) \cos θ \cot (π + θ)} = \frac{(\cos (2 π + θ)) (\frac{1}{\sin (2 π + θ)}) (\frac{\sin (\frac{π}{2} + θ)}{\cos (\frac{π}{2} + θ)})}{(\frac{1}{\cos (\frac{π}{2} + θ)}) (\cos θ) (\frac{\cos (π + θ)}{\sin (π + θ)})} = \frac{(\cos (2 π + θ)) (\frac{1}{\sin (2 π + θ)}) \sin (\frac{π}{2} + θ)}{(\cos θ) (\frac{\cos (π + θ)}{\sin (π + θ)})} = \frac{\cos (π + (π + θ)) (\frac{1}{\sin (π + (π + θ))}) \sin (\frac{π}{2} + θ)}{(\cos θ) (\frac{\cos (π + θ)}{\sin (π + θ)})} = \frac{- \cos (π + θ) (- \frac{1}{\sin (π + θ)}) \cos θ}{(\cos θ) (\frac{- \cos θ}{- \sin θ})} (S i n c e, \sin (π + θ) = - \sin θ a n d \cos (π + θ) = - \cos θ) = \frac{\cos θ (\frac{1}{\sin θ)}) \cos θ}{(\cos θ) (\frac{\cos θ}{\sin θ})} = 1 H e n c e, \frac{\cos (2 π + θ) \cos e c (2 π + θ) \tan (\frac{π}{2} + θ)}{\sec (\frac{π}{2} + θ) \cos θ \cot (π + θ)} = 1$

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