Question

If tan A=a tan B and sin A =b din B ,prove that cos² A=b²-1÷a²-1

Answer 1

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BrainlyHelper

BrainlyHelper

30.01.2018

Math

Secondary School

+13 pts

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If tan A = n tan B and sin A = m sin B , then prove that cos ² A = m²-1 / n²-1.

(Class 10 Maths Sample Question Paper)

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THE BRAINLIEST ANSWER!

nikitasingh79

nikitasingh79 Genius

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

HOPE THIS WILL HELP YOU.