prove that
(1- cos A)(1+sec A)=tan Asin A
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taking LHS = (1-cos A) (1+sec A)
= (1-cos A) (1+ 1/cos A)
= (1-cos A) ( cos A+ 1 / cos A)
= (1-cos A) (1+cos A /cos A)
= 1 - cos²A/cos A
= sin²A / cos A
= sin A * sin A/ cos A
= sin A * tan A
so, LHS = RHS
HENCE PROVED.
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