If sin(32)=x , then sin(4) cos(4) cos(8) cos(16)=..............
1 answer:
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.
To learn more on trigonometric functions, we kindly invite to check this verified question: brainly.com/question/6904750
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