First slide

Trigonometric Identities

Question

If $a \cos^{3} α + 3 a \cos α \sin^{2} α = m$ and $a \sin^{3} α + 3 a \cos^{2} α \sin α = n$ then ${(m + n)}^{2 / 3} + {(m - n)}^{2 / 3} =$

Moderate

A

$2 a^{2}$
B

$2 a^{1 / 3}$
C

$2 a^{2 / 3}$
D

$2 a^{3}$

Solution

$m + n = a {(\cos α + \sin α)}^{3},$ $m - n = a {(\cos α + \sin α)}^{3}$

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