The value of (secA+tanA)(1-sinA) is equal to :
We know that secA=1cosA,tanA=sinAcosA
Now we put these values in the brackets
(secA+tanA)(1-sinA)=(1cosA+sinAcosA)(1-sinA)
⇒(1+sinAcosA)(1-sinA1)=12-sin2AcosA((a-b)(a+b)=a2-b2)
We know that cos2A+sin2A=1,1-sin2A=cos2A
Now after putting the values the we get
⇒1-sin2AcosA=cos2AcosA=cosA
Hence, (secA+tanA)(1-sinA)=cosA