If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using double angle trigonometric functions.
How to simplify an expression by trigonometric expressions
Trigonometric expressions are formulas that utilize trigonometric functions. Trigonometric functions are a kind of trascendental functions, that is, functions that cannot be described in algebraic terms.
In this question we must simplify a given expression by using the following trigonometric formula:
sin 2x = 2 · cos x · cos x (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 double angle trigonometric functions. [tex]\blacksquare[/tex]
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