Prove the following60. If tan A n tan B and sin Am sin Bprove that cos

1.	Prove the following60. If tan A n tan B and sin Am sin Bprove that cos2 A = m-1ŕ¸ŕ¸ľ
Answer» 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 Btan B = 1/n tan A Cot B = n /tan A [ cot B = 1/tan B] sin A = m sinB sin B = 1/m sinAcosec 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 = 1m² - n²cos²A = sin²Am² - n²cos²A = 1- cos²A [sin²A = 1- cos²A] m² -1 = n²cos²A - cos²Am² - 1 = cos ²A(n² -1) cos²A = m² -1/ n²-1 Like my answer if you find it useful!

Prove the following60. If tan A n tan B and sin Am sin Bprove that cos2 A = m-1ŕ¸ŕ¸ľ

Answer»

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 Btan B = 1/n tan A

Cot B = n /tan A [ cot B = 1/tan B]

sin A = m sinB sin B = 1/m sinAcosec 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 = 1m² - n²cos²A = sin²Am² - n²cos²A = 1- cos²A

[sin²A = 1- cos²A]

m² -1 = n²cos²A - cos²Am² - 1 = cos ²A(n² -1)

cos²A = m² -1/ n²-1

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