1.

. Sing — Cos¢ +1 _Sing +1Sing + Cos¢p—1 Cos¢

Answer»

(sinθ - cosθ +1 )/(sinθ +cosθ -1)

dividing numerator and denominator by cosθ

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

As, sec²θ- tan²θ = 1(secθ -tanθ)(secθ +tanθ) = 1

putting this in numerator,[(tanθ + secθ -(sec²θ- tan²θ)]/(tanθ - secθ+1)=[(tanθ + secθ) -(secθ- tanθ)(secθ+tanθ)]/(tanθ - secθ+1)=(tanθ+secθ)[1- (secθ - tanθ)]/(tanθ - secθ+1)=(tanθ+secθ)[1- secθ + tanθ)]/(tanθ - secθ+1)=(tanθ+secθ)

Now, multiplying and dividing by(secθ- tanθ)[(tanθ+secθ)×(secθ- tanθ)]/(secθ- tanθ)=(sec²θ- tan²θ)/(secθ- tanθ)= 1/(secθ- tanθ)=1/1/cos-sin/cos=sin+1/cos


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