SOLUTION: Hi tutors. Please help me verify that this equation is an identity. [(sin^3 A) + (cos^3 A)]/(sinA +cosA) = 1 - (sinA)(cosA) Please show the steps if you can so that I can

Question 602472: Hi tutors. Please help me verify that this equation is an identity.
[(sin^3 A) + (cos^3 A)]/(sinA +cosA) = 1 - (sinA)(cosA)

Please show the steps if you can so that I can follow how to arrive at the correct answer. Thank you so much.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Hi tutors. Please help me verify that this equation is an identity.
[(sin^3 A) + (cos^3 A)]/(sinA +cosA) = 1 - (sinA)(cosA)
**
Use sum of cubes formula to solve:
x^3+y^3=(x+y)(x^2-xy+y^2)
For given problem:
Start with left side:
(sin^3+cos^3)/(sin+cos)
=[(sin+cos)(sin^2-sincos+cos^2)]/(sin+cos)
sin^2+cos^2=1
(sin+cos) cancels out
=1-sincos
verified:
left side=right side
RELATED QUESTIONS
Please prove: ((cos2A)/(cosA+sinA)^3) =... (answered by Cromlix)

Prove that the equation is an identity: sinA(sinA + cotA) = 1 + cosA - cos^2 A... (answered by stanbon)

Dear Sir/Madam, Please help me solve this problem: Show that (1-sinA+cosA)^2 =... (answered by MathLover1)

Prove that: ((cos2A)/(cosA+sinA)^3) =... (answered by Cromlix)

Please help me with this question,If SinA=2/3,and A is obtuse, find the exact value of,... (answered by MathLover1,ikleyn)

Prove that : 1. (cscA-1)/(cscA+1) = (1-sinA)/(1+sinA) 2. (secA/cscA)+(sinA/cosA) =... (answered by Edwin McCravy)

If {{{(sinA+cosA)/sinAcosA=1/3}}} What is the value of... (answered by ikleyn)

if CosA+SinA=1, show that CosA-SinA=�1 (answered by Edwin McCravy)

show that... (answered by solve_for_x)