Question

show that sin³theta + cos³theta/sin theta + cos theta =1-sin theta cos theta​

Answer 1

Answer:

=( sin^3 A + cos^3A )/(sinA + cosA)

= (sinA + cosA)^3 - 3sinAcosA(sinA+cosA)

--------:---:-------. ----------------------------------

(sinA + cosA). (sinA + cosA)

= (sinA + cosA)^2 - 3sinAcosA

= sin^2A + cos^2A + 2sinAcosA - 3sinAcosA

= 1 - sinAcosA

RHS proved