Question

(1-cos168°)(1-cos75°)(1-cos105°)(1-cos165°)=1/16​

Answer 1

Here is answer

Explanation:

The given equation states that the product of four quantities is equal to 1/16. Each of these quantities is of the form 1 - cos(x), where x is an angle in degrees.

We can use the fact that cos(x) = cos(180 - x) to rewrite each of the four quantities as 1 - cos(180 - x). This gives us:

(1 - cos(12 - x))(1 - cos(105 - x))(1 - cos(75 - x))(1 - cos(15 - x)) = 1/16

We can simplify this equation as follows:

(cos(x) - 1)(cos(x - 105) - 1)(cos(x - 75) - 1)(cos(x - 15) - 1) = 1/16

We can then use the identity cos(x) = -cos(180 - x) to further simplify the equation:

(-cos(x) + 1)(-cos(x - 105) + 1)(-cos(x - 75) + 1)(-cos(x - 15) + 1) = 1/16

This simplifies to:

(cos(x) + 1)(cos(x - 105) + 1)(cos(x - 75) + 1)(cos(x - 15) + 1) = 1/16

This is the final form of the equation. It states that the product of four quantities, each of which is equal to the cosine of a certain angle plus 1, is equal to 1/16.