VeryifingTrigonometric Identities?

Question

How would I go about verifying this problem?

sin^3 β + cos^3 β / sin β + cos β = 1 - sin β cos β

Answer 1

sin^3 β + cos^3 β = (sinβ + cosβ)(sin^2β + cos^2β - sinβcosβ)
= (sinβ + cosβ)(1 - sinβcosβ)

sin^3 β + cos^3 β / sin β + cos β
= (sinβ + cosβ)(1 - sinβcosβ)/( sin β + cos β)
= 1 - sinβcosβ

Answer 2

Google these:
Pythagorean Identities
Double Angle Identites
Power Reducing Formula

That should do the trick :)

Answer 3

Use the factoring: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Answer 4

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Answer 5

You have to treat this like

(x^3 + y^3)/(x + y) = 1 - xy

Then just plug in sin(B) for x and cos(B) for y, after you have simplified it.

(sin(B)^3 + cos(B)^3)/(sin(B) + cos(B)) = 1 - sin(B)cos(B)

((sin(B) + cos(B))(sin(B)^2 - sin(B)cos(B) + cos(B)^2))/(sin(B) + cos(B)) = 1 - sin(B)cos(B)

sin(B)^2 - sin(B)cos(B) + cos(B)^2 = 1 - sin(B)cos(B)

sin(B)^2 + cos(B)^2 - sin(B)cos(B) = 1 - sin(B)cos(B)

(sin(B)^2 + cos(B)^2) - sin(B)cos(B) = 1 - sin(B)cos(B)

1 - sin(B)cos(B) = 1 - sin(B)cos(B)