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Alex_Xolod [135]
2 years ago
7

If sin(32)=x , then sin(4) cos(4) cos(8) cos(16)=..............

Mathematics
1 answer:
svp [43]2 years ago
6 0

If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using <em>double angle trigonometric</em> functions.

<h3>How to simplify an expression by trigonometric expressions</h3>

<em>Trigonometric</em> expressions are formulas that utilize <em>trigonometric</em> functions. <em>Trigonometric</em> functions are a kind of <em>trascendental</em> functions, that is, functions that cannot be described in <em>algebraic</em> terms.

In this question we must simplify a given expression by using the following trigonometric formula:

<em>sin 2x = 2 · cos x · cos x</em>   (1)

Now we proceed to expand the expression given:

x = sin 32

x = 2 · sin 16 · cos 16

x = 4 · sin 8 · cos 8 · cos 16

x = 8 · sin 4 · cos 4 · cos 8 · cos 16

Thus,

sin 4 · cos 4 · cos 8 · cos 16 = x/8

If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using <em>double angle trigonometric</em> functions. \blacksquare

To learn more on trigonometric functions, we kindly invite to check this verified question: brainly.com/question/6904750

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