Question

The value of 12sin40°-16sin^3 40°?

Answer 1

$The \:value \: of \: 12sin 40\degree - 16 sin^{3} 40\degree \\= 4(3sin 40\degree - 4 sin^{3})\\= 4 \sin ( 3 \times 40)$

$\boxed {\pink { Since, 3sin A - 4sin^{3} A = sin 3A }}$

$= 4 \times sin 120\degree \\ = 4 sin( 90 + 30 ) \\= 4 cos 30\degree \\= 4 \times \frac{\sqrt{3}}{2} \\= 2\sqrt{3}$

Therefore.,

$\red{The \:value \: of \: 12sin 40\degree - 16 sin^{3} 40\degree } \\\green {= 2\sqrt{3} }$

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