Question

help me friends.....

best one will be marked as brainliest......

Answer 1

Hope it will help you .

Answer 2

(sin³ theta + cos³ theta / sin theta + cos theta) + sin theta * cos theta

[since a³ + b³ = ( a + b )( a² + b² + ab)]

so

the question can be written as

[(sin theta + cos theta ) ( sin² theta + cos² theta - sin theta * cos theta ) / ( sin theta + cos theta )] + sin theta * cos theta

( sin theta + cos theta ) and ( sin theta + cos theta ) gets cancelled

so we get

sin² theta + cos² theta - sin theta * cos theta + sin theta * cos theta

[as we know that sin² theta + cos² theta = 1 ]

and

sin theta * cos theta - sin theta * cos theta = 0

so we get

1 - 0

= 1

So we get that (sin³ theta + cos³ theta / sin theta + cos theta) + sin theta * cos theta = 1

Hope this helps you