Prove that : (90^ - ) (90^ - ) (90^ - ) e c =1 - Vidyadip

Question

Prove that : $\frac{\sin \left(90^{\circ}-\theta\right) \tan \left(90^{\circ}-\theta\right) \sec \left(90^{\circ}-\theta\right)}{\cos e c \theta \cdot \cos \theta \cdot \cot \theta}=1$

✓

Answer

LHS = $\frac{\sin \left(90^{\circ}-\theta\right) \tan \left(90^{\circ}-\theta\right) \sec \left(90^{\circ}-\theta\right)}{\operatorname{cosec} \theta \cdot \cos \theta \cdot \cot \theta}=1$
$ =\frac{\operatorname{cosec} \theta \cdot \cos \theta \cdot \cot \theta}{\operatorname{cosec} \theta \cdot \cos \theta \cdot \cot \theta}$
$=1$
$=\text { RHS } $
Hence proved.

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