Question

Sin³ 0 +cos³0 / sin 0+ cos 0 = 1-sin 0 cos 0

Answer 1

Explanation:

SHOW THAT:

sin³ 0 +cos³0 / sin 0+ cos 0 = 1 - sin 0 cos 0

Now, using the identity a^3 + b^3 = (a + b)(a^2 + b^2 - ab):

sin³ 0 +cos³0 = (sin 0 + cos 0)(sin² 0 +cos²0 - sin0 cos 0)

As sin² 0 +cos²0 = 1 we have:

sin³ 0 +cos³0 = ( sin 0 + cos 0)(1 - sin0 cos 0)

So we can write the left side of the original expression as

( sin 0 + cos 0)(1 - sin0 cos 0) / (sin 0+ cos 0)

= 1 - sin0 cos 0 = Right side

= and we are done!.