Question

Please solve this if anyone want 50 points

Answer 1

Hi , 

LHS = ( sinθ - cosθ +1 )/ ( sinθ + cosθ - 1 )

        =  ( sinθ  - cosθ + 1 ) (sinθ +cosθ + 1 )/( sinθ + cosθ - 1)(sinθ+cosθ+1)

        = [(sinθ +1) -cosθ][(sinθ+1)+cosθ]/[(sinθ+cosθ)-1][(sinθ+cosθ)+1]

        = [ (sinθ + 1 )² - cos²θ ] / [ (sinθ +cosθ)² - 1²]

        = [ sin²θ+2sinθ+1 -cos²θ ] / [ sin²θ+cos²θ+ 2sinθcosθ -1]

       = [ sin²θ + 2sinθ+ sin²θ] / [ 1 +2sinθcosθ -1 ]

       =[ 2sin²θ+ 2sinθ] / ( 2sinθ cosθ )

       = [ 2sinθ ( sinθ + 1 ) ] / ( 2sinθcosθ )

       = ( sinθ + 1 ) / ( cosθ )

       = [(sinθ / cosθ+ 1 / ( cos θ )]

       = ( tanθ+ sec θ)

       = [ ( sec θ + tan θ ) ( sec θ - tan θ)] / ( sec θ - tan θ)

       = ( sec² θ - tan² θ ) / ( sec θ- tan θ)

       =  1 / ( secθ - tan θ )

       = RHS

Answer 2

Your answer in the above attachment