Question

value of 12 sin 40° -16 sin^3 40°
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Answer 1

Answer:

4[3sin 40°-4sin^3 40°]

=4[sin120°]

=4[v3 /2)=2 v3

Answer 2

Answer:

The value of the given expression is

$12 sin 40 -16 sin^{3} 40=2\sqrt{3}$

Step-by-step explanation:

The given trigonometric expression is

$12 sin 40 -16 sin^{3} 40$

We shall solve the above expression by using the concept of multiple and sub multiple angles.

Taking 4 as common factor in above expression,we get

$4(3sin40-4sin^{3}40)$

The above expression is of the form $3sin\theta-4sin^{3}\theta$ which is equal to the sine of multiple angle as shown

$sin3\theta=3sin\theta-4sin^{3}\theta$

Hence our expression becomes

$4(sin(3\times40))=4sin120\\=4sin(180-60)=4sin60=2\sqrt{3}$

Hence the value of the given expression is

$12 sin 40 -16 sin^{3} 40=2\sqrt{3}$

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