Question

If the sides of a triangle ABC are given as 4, 5, 7 respectively then cotB/2 cotc/2 equals ​

Answer 1

Answer:

1.56

Explanation :

To find the value of cot(B/2) / cot(C/2), we need to use the law of cosines to find the value of the cosine of angle B and angle C, and then use the trigonometric identity cot(x) = 1/tan(x) to find the cotangent of B/2 and C/2.

First, let's use the law of cosines to find the value of cos(B):

cos(B) = (a^2 + c^2 - b^2) / (2ac)

where a, b, and c are the sides of the triangle, and B is one of the angles.

Substituting the values for the sides of the triangle:

cos(B) = (4^2 + 7^2 - 5^2) / (2 * 4 * 7) = 0.6

Next, let's use the law of cosines to find the value of cos(C):

cos(C) = (a^2 + b^2 - c^2) / (2ab)

Substituting the values for the sides of the triangle:

cos(C) = (4^2 + 5^2 - 7^2) / (2 * 4 * 5) = 0.2

Now, let's use the trigonometric identity to find the cotangent of B/2 and C/2:

cot(B/2) = 1 / tan(B/2)

cot(C/2) = 1 / tan(C/2)

Using the identity tan(x/2) = sqrt((1 - cos(x)) / (1 + cos(x))), we can find the value of tan(B/2) and tan(C/2):

tan(B/2) = sqrt((1 - cos(B)) / (1 + cos(B))) = sqrt((1 - 0.6) / (1 + 0.6)) = 0.74

tan(C/2) = sqrt((1 - cos(C)) / (1 + cos(C))) = sqrt((1 - 0.2) / (1 + 0.2)) = 1.15

Finally, we can use the values of tan(B/2) and tan(C/2) to find the value of cot(B/2) / cot(C/2):

cot(B/2) / cot(C/2) = 1 / tan(B/2) / 1 / tan(C/2) = 1 / (0.74) / 1 / (1.15) = 1.15 / 0.74 = approximately 1.56.

To know more about the concept please go through the links :

https://brainly.in/question/5111275

https://brainly.in/question/1086114

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