Question

if tan a is equal to 2 and 10 B and sign is equal to M Sin B prove that cos squared is equal to M squared minus ÷ 1 and square minus one.​

Answer 1

Answer:

Solution:

In this question we have to find cos²A in terms of m and n , so we have to eliminate ∠B  from the given relations.

tan A = n tan B

tan B = 1/n tan A

Cot B = n /tan A  [ cot B = 1/tan B]

sin A = m sinB

sin B = 1/m sinA

cosec B = m / sinA     [sinB = 1/cosecB]

cosec²A - cot²B =1

Substitute the value of cot B and cosec B in the above relation.

(m / sinA)² - (n /tan A)²

(m² / sin²A) - (n² /tan² A)

(m² / sin²A) - (n² /(sin²A / cos²A))

[ tan A = sinA / cosA]

(m² / sin²A) - n²cos²A / sin²A = 1

m² - n²cos²A  = sin²A

m² - n²cos²A  = 1-  cos²A

[sin²A = 1-  cos²A]

m² -1  = n²cos²A -  cos²A

m² - 1 = cos ²A(n² -1)

cos²A = m² -1/ n²-1