Question

prove that sin^3 theta +cos^3 theta / sin theta + cos theta = 1-sin theta.cos theta
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Answer 1

sin^3 + Cos^3 = ( sin + cos)( sin^2 - sin cos + cos^2)

As sin^2 + cos^2 = 1

so ( sin + cos)( 1 - sin cos)

Now ( sin + cos)( 1- sin cos)/ ( sin + cos)

= ( 1 - sin cos)

Answer 2

hey mate here is your answer
let theta =x
(sin³x+cos³x)/sinx+cosx
(sinx+cosx)(sin²x+cos²x-sinx.cosx)/sinx+cosx
sin²x+cos²x-sinx.cosx...........(identity)
1-sinx.cosx
hence proved
hope it will help you
mark me brainliest