(1-cos A)(1+ sec A)= tan A × sin A​

Answers (1)

(1 - \cos A) (1+ \sec A) = \tan A \sin A\\ LHS = (1- \cos A)(1+ \frac{1}{\cos A})\\ = \frac{(1- \cos A)(1+ \cos A)}{\cos A}\\ = \frac{1- \cos^2 A}{\cos A}\\ =\frac{ \sin^2 A}{\cos A}\\ =\tan A \sec A = RHS

Hence proved 

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