Question

1 - sin^3A/(sinA + cosA) - Cos^3A/(sinA + cosA) =?​

Answer 1

Answer:

Step-by-step explanation:

Trigonometry,

We have to prove that

(sin³A+cos³A/sinA+cosA) + (sin³A-cos³A/sinA-cosA)=2

LHS = (sin³A+cos³A/sinA+cosA) + (sin³A-cos³A/sinA-cosA)

= {(sinA+cosA)(sin²A+cos²A-sinA.cosA)}/(sinA+cosA) + {(sinA-cosA)(sin²A+cos²A+sinA.cosA)}/(sinA-cosA)

= (sin²A+cos²A-sinA.cosA) + (sin²A+cos²A+sinA.cosA)

= 1-sinA.cosA+1+sinA.cosA

= 1+1

= 2 = RHS [proved]

That's it

Hope it helped (^_^メ)

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