Question

tana+ seca- 1× tana+1+seca=2sina÷1-sina

Answer 1

tanA+secA-1)(tanA+1+secA)=2sinA/1-sinA 
secA=1/cosA 
secA-1=(1-cosA)/cosA 
tanA+secA-1=(sinA-cosA+1)/cosA 

(tanA+1+secA)=(sinA+cosA+1)/cosA 

multiply 
[(sinA-cosA+1)/cosA][(sinA+cosA+1)/cosA... 
[sin^2A+sinAcosA+sinA-sinAcosA-cos^2A-c... 
=[sin^2A-cos^2A+2sinA+1]/cos^2A 
we have sin^2A+cos^2A=1=>1-cos^2A=sin^2A 

=>[2sin^2A+2sinA]/cos^2A 
and cos^2a=1-sin^2A=(1+sinA)(1-sinA) 

2sin^2A+2sinA can be written as: (1+sinA)(2sinA) 
=>(1+sinA)(2sinA)/(1+sinA)(1-sinA) 
=2sinA/1-sinA