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Find:\(\cfrac{sin(t - 2 \pi)}{sec(\frac{\pi}{2}-t)} \) |
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Answer» \(\cfrac{sin(t - 2 \pi)}{sec(\frac{\pi}{2}-t)} \) = \(\cfrac{sin(-(2\pi-t))}{cosect}\) (∵ sec (π/2 - θ) = cosec θ) =\(\cfrac{-sin(2\pi-t)}{cosec\, t} \) (∵ sin (-θ) = -sinθ) = \(\cfrac{-(-sin\,t)}{cosec\, t} \) (∵ sin (2π - θ) = -sinθ) = sin t / cosec t = sin t sin t \((∵\cfrac{1}{cosecθ}=sinθ)\) = sin2 t Hence, \(\cfrac{sin(t-2π)}{sec(\frac{\pi}2-t)}=sin^2 t\) |
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