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prove that secA + tanA - 1 / tanA - secA + 1 = cosA/ 1 - sinA

prove that secA + tanA - 1 / tanA - secA + 1 = cosA/ 1 - sinA

Grade:10

1 Answers

samyak katiyar
31 Points
one month ago
(secA+tanA-(sec^2 A - tan ^2A)) )/tanA-secA+1) as sec^2 A= 1 + tan ^2 A so 1= sec^2 A - tan ^2 A 
= (sec A + tan A - (sec A + tan A) ( sec A - tan A)) / ( tanA-secA+1) 
= ( sec A + tan A ) ( 1- (sec A - tan A)/ ( tanA-secA+1) 
= (sec A + tan A)/(+ tan A - sec A)/(tan A- sec A+ 1) 
= (sec A + tan A) 
= 1/cos A + sin A/ cos A 
= (1+ sin A)/ cos A 
= (1 + sin A )(1- sin A)/(cos A (1- sin A)) 
= (1- sin ^2 A/(cos A (1- sin A)) 
= cos ^2 A / (cos A (1- sin A)) 
= cos A /(1- sin A) 

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