Question

If,

⇒ a cos³∅ + 3a sin²∅ cos∅= m

And,

⇒ a sin³∅ + 3a sin∅ cos²∅= n

Prove that :

⇒ ( m + n )⅔ + ( m - n )⅔ = 2a⅔

Answer 1

I hope I have done it in a appropriate manner,
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This is my explanation of you nice and a little bit tricky question,
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And I hope I am able to make yourself in a conditions to understand this question,
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Thanks,

# ☮️PEACE

Answer 2

Hi!

Here is your answer

m + n = acos3x + 3a cosx sin2x + asin3x + 3a cos2xsinx = a(sinx + cosx)3

(m + n)2/3 = a2/3 (sinx + cosx)2

m – n = acos3x + 3a cosx sin2x – asin3x – 3a cos2xsinx = a(cosx + sinx)3

(m – n)2/3 = a2/3 (cosx – sinx)2

(m + n)2/3 + (m – n)2/3 = a2/3 (sinx + cosx)2 + a2/3 (cosx – sinx)2 =

a2/3[(sinx + cosx)2 + (cosx – sinx)2] = 2a2/3

Hoping it helps

:D