Question

Show that

sin³A+cos³A/sinA+cosA=1-sinAcosA ​

Answer 1

Answer:

The principal trick, here is to recall that 1 = sin^2 A + cos^2 A .

The other term in the parentheses, being second degree in sin A and cos A , suggests that that might be useful.

Alternatively, start with the RHS, a difference of two cubes, which has a standard factorisation:

a^3 + b^3 = (a + b) (a^2 - ab + b^2) .

So sin^3 A + cos^3 A = (sin A + cos A) (sin^2 A - sin A cos A + cos^2 A)

= (sin A + cos A) (1 - sin A cos A) ,

Answer 2

Answer:

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