Question

If sinx+cosx=a then what is sin^3 x +cos^3 x in terms of "a"?

Answer 1

ha,!! I can imitate oldrinbataku to solve this problem.

Answer 2

sin^3 + cos^3 = (sin + cos) (sin^2 -sincos +cos^2) = (sin + cos) ( 1-sin cos)

Answer 3

and (sin + cos)^2 = sin^2 + cos ^2 + 2sin cos = 1 + 2 sincos = a^2
so, sin cos = (a^2 -1)/2
replace all
(sin + cos) (1-sin cos) = a (1 - (a^2 -1) /2)
let write it in neat
\[sin^3x+cos^3 x= a(1-\dfrac{a^2-1}{2})\\\]
=\(\dfrac{2a-a^2+1}{2}\)

Answer 4

@oldrin.bataku check your mentee's work, hihihi