Rewrite the expression sin2x + cosx

Question

Rewrite the expression sin2x + cosx as one involving only sinx and cosx (they can be squared, but they may not have a 2x in them).

Answer 1

sin2x = 2sinxcosx by the double angle formula

sin2x + cosx

= 2sinxcosx + cosx which is probably the answer you want, or also

= cosx(2sinx +1)

or if you want just sinx, cosx= + or - square root of (1-(sinx)^2)

= [+ sqr(1-(sinx)^2](2sinx+1)