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
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-> 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
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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
(