Question

In a plane triangle, find the maximum value of cos A cos B cos C​

Answer 1

Answer:

60

Step-by-step explanation:

The maximum value can be obtained cos a = cos b= cos c. You have to add the three values and they are equal . b and then add all the three values as a+b+c = 180. So a= b= c =60.

Answer 2

The largest value is 1/8

Given

• cos A cos B cos C

To find

• the maximum value

Solution

we are given with the product of trigonometric functions and are asked to estimate the maximum value of the given trigonometric function.

the angles included in the trigonometry functions that is, A, B,C are from a plane triangle,

therefore,

A +B + C = 180 ( angle sum property of the triangle)

The given trigonometry function cosx has the maximum value when the angle included in it is the smallest, therefore we have to make the three angles smallest as possible.

The smallest angles are possible only when,

A = B = C

A +B + C = 180

3A = 180°

A = 60°

A = B = C = 60°

cos60 = 1/2

Therefore, the largest value of cos A cos B cos C

or cos60 × cos60 × cos60

or, 1/2 × 1/2 × 1/2

or, 1/8

The largest value is 1/8

#SPJ3

learn more,

https://brainly.in/question/14442467

https://brainly.in/question/12855224