8-4

sinA tanA+sin(90degrees-A)
=sinA*sinA/cosA+cosA
=sin^2A/cosA+cosA/1= sin^2A+cos^2A/cosA=1/cosA=secA


To solve these problems, you have to know the formulas.  Sin^2 A+ cos^2 A=1, sec A= 1/cos A, Tan A= sin A/cos A, and Sin90degrees-A)=cos A in these problems, you have to memorize those functions in order to solve this problem.  So, first you put sin A times sinA/cosA because one of our formulas that we have to know is tan A=sinA/cosA. Then, you add cosA.  Next, you look and see if you can cancel out anything.  You can't in this problem, so we multiply sinA times sinA and get sin^2 A/cos A.  Then, you add cos A to that.  You get sin^2 A + cos^2A over cosA.  Sin^2 A+Cos^2 A=1 from the formulas we are supposed to memorize, so then you have 1/cos A and that equals secA from another formula we are supposed to know.