Question

De value of cos1 cos2 cos 3 ....cos 180 is =?

Answer 1

value of equation above is 0. because in this cos 90 is also being multiplied. since value of cos 90 is 0 so whole equation becomes 0.
=cos1.cos2.....cos90...cos 180
= cos 1. cos 2.... (0)...cos 180
= 0 answer

Answer 2

cos1 cos2 cos 3 .... cos 180 = 0

Step-by-step explanation:

The cos trigonometric function is positive in first and fourth quadrants in the coordinate axes.

Let us consider the cosine wave graph as given in the figure below.

$\cos 0=1$

$\cos 30=\sqrt{3 / 2}$

$\cos 45=1 / \sqrt{2}$

$\cos 60=1 / 2$

$\cos 90=0$

cos decreases from 1 to 0 in the interval [0, Π/2]

Again decreases to -1 and increases to 1 as shown in the figure.

So, value of cos is 0 at Π/2, 3Π/2, … multiples of Π/2.

Also, cos value is 1 at cos0, cos2Π, ….. even multiples of Π

Cosine value is -1 at cosΠ, cos3Π,….. odd multiples of Π

Now, consider the given problem

cos1 cos2 cos 3 ....cos 180 = cos1cos2cos3……..cos90….cos180

cos1 cos2 cos 3 ....cos 180 = cos1cos2cos3 ……… (0) ……… (-1)

As anything multiplied with 0 will be 0

cos1 cos2 cos 3 ....cos 180 = 0