Math, asked by surabhiver123, 11 months ago

If tan A = n tan B and sin A = m sin B, prove that cos^2 A= (m^2 -1) / (n^2 -1).

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Answers

Answered by khanaffanullah

Answer:

m(cosAcosB-sinAsinB) = n(cosAcosB + sinAsinB)

(m-n)cosAcosB = (n+m)sinAsinB

(sinAsinB)/(cosAcosB) = (m-n)/(m+n)

sinA/cosA = [(m-n)/(m+n)]cosB/sinB

tanA = [(m-n)/(m+n)]cotB

QED

Step-by-step explanation:

m(cosAcosB-sinAsinB) = n(cosAcosB + sinAsinB)

(m-n)cosAcosB = (n+m)sinAsinB

(sinAsinB)/(cosAcosB) = (m-n)/(m+n)

sinA/cosA = [(m-n)/(m+n)]cosB/sinB

tanA = [(m-n)/(m+n)]cotB

QED

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