Question

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

Answer 1

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. $\blacksquare$

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