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How do you simplify $4 sin 21 cos 21$ $4 sin 21 cos 21$ ?

1 Answer

Alan P. · Johnson Z.

Nov 23, 2015

$4 sin (21^{\circ}) cos (21^{\circ}) = 2 sin (42^{\circ}) \approx 1.328$ $4sin(21^@)cos(21^@) = 2sin(42^@) ~~ 1.328$

Explanation:

Double angle formula for sine function:
$XXX 2 sin (θ) cos (θ) = sin (2 θ)$ $color(white)("XXX")2sin(theta)cos(theta) = sin(2theta)$

$4 sin (21^{\circ}) (cos (21^{\circ})) = 2 (sin (2 \times 21^{\circ})) = 2 sin (42^{\circ})$ $4sin(21^@)(cos(21^@)) = 2(sin(2xx21^@)) = 2sin(42^@)$

Using a calculator:
$XXX 2 sin (42^{\circ}) = 1.328$ $color(white)("XXX")2sin(42^@) = 1.328$

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