Question

The value of (1+cos pi/6)(1+cos pi/3)(1+cos 2pi/3)(1+cos 7pi/6) is

Answer 1

hope you will understand

Answer 2

Concept:

Trigonometry is the relation between the angles of the triangle.

We can use trigonometric functions to find the length of the sides of the triangle.

Trigonometric functions are sine function, cosine functions,  tangent function, co-tangent function, secant function and co-secant function.

Given:

We are given that:

(1+cos π/6)(1+cos π/3)(1+cos 2π/3)(1+cos 7π/6)

Find:

We need to find the value of the trigonometric function.

Solution:

We will do this by putting the value of angles in the trigonometric function that is given to us.

Putting π=180° in the function, we get:

(1+cos 30°)(1+cos 60°)(1+cos 120°)(1+cos 210°)

This can be further solved as:

=(1+√3/2)(1-√3/2)(1+1/2)(1-1/2)

Solving the function, we get:

=(1-3/4)(1-1/4)

(1/4)(3/4)

=3/16

Therefore, we get the value of (1+cos π/6)(1+cos π/3)(1+cos 2π/3)(1+cos 7π/6) as 3/16.

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