SOLUTION: Prove the identity {{{ (1+sinx )/cosx + cosx/(1+sinx ) = 2/cosx }}}

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the identity {{{ (1+sinx )/cosx + cosx/(1+sinx ) = 2/cosx }}}      Log On


   

Question 415178: Prove the identity
+%281%2Bsinx+%29%2Fcosx+%2B+cosx%2F%281%2Bsinx+%29+=+2%2Fcosx+
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

+%281%2Bsinx+%29%2Fcosx+%2B+cosx%2F%281%2Bsinx+%29+=+2%2Fcosx+   |MULTIPLYING each term by cosx(1 + sinx)

+%281%2Bsinx%29%281%2B+sinx%29++%2B+cosx%2Acosx++=+2%281%2Bsinx%29cosx%2Fcosx 

+1%2B2sinx+%2B+sinx%5E2++%2B+cosx%5E2++=+2%281%2Bsinx%29   |sinx^2 + cosx^2 = 1

        1+ 2sinx + 1 = 2 + 2sinx

        2 + 2sinx = 2 + 2sinx