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(tan a +sec a - 1) (tan a + 1 +sec a) =2 sin a/ 1 - sin a

(tan a +sec a - 1) (tan a + 1 +sec a) =2 sin a/ 1 - sin a
 
 
 
 
 

Grade:6

1 Answers

Arun
25750 Points
5 years ago
tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cos A

multiply LHS by cosA /cosA to get 
(sinA+1-cosA) / (sinA-1+cosA) 

multiply again by cosA/cosA to get 
(sinA.cosA+cosA-cos^2A) / cosA(sinA-1+cosA) 

= ( cosA(1+sinA) - (1-sin^2A) ) / cosA(sinA-1+cosA) 
= ( cosA(1+sinA) - (1+sinA)(1-sinA) ) / cosA(sinA-1+cosA) 
= ( (1+sinA)(cosA-1+sinA) ) / cosA(sinA-1+cosA) 
= (1+sinA)/cosA
 
Regards
Arun

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