Question
If acos 3 θ + 3asin 2 θcosθ = m
and asin 3 θ + 3asinθcos 2 θ = n, then find the value of (m + n) 2/3 + (m – n) 2/3 .Solution
We have, a cos3θ + 3a sin2θ cosθ = m and a sin3 θ + 3a sin θ cos2θ = n
put θ = 45º, then
a/2√2 + 3a/2√2 = m and a/2√2 + 3a/2√2 = n
⇒ m = n = √2 also, (m + n) 2\3 +(m − n) 2\3 = (√2a + √2a) 2\3 + 0
= (2√2a) 2\3 = (2 3\ 2 .a) 2\3 = 2a 2\3
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