verify: sin^3x + cos^3x/ sinx + cosx = 1 - 1/2sin2x

Answer 1

Recall that A³ + B³ factors as (A + B)(A² - AB + B²), sin²x + cos²x = 1, and sin(2x) = 2sinxcosx.

So, (sin³x + cos³x) / (sinx + cosx) = (sinx + cosx)(sin²x - sinxcosx + cos²x) / (sinx + cosx)

= sin²x - sinxcosx + cos²x = 1 - sinxcosx = 1 - (1/2)(2sinxcosx) = 1 - (1/2)sin(2x)

Answer 2

I punched in the formula. I set the angle at 30°; the closest I got was x=12.2=.2084; need to hit 0.