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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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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