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If cosA/cosB=n and sinA/sinB=m,show that (m*m-n*n)*sinB*sinB=1-(n*n) |
(m*m-n*n)*sinB*sinB = ((sin^2A/sin^2B)-(cos^2A/cos^2B))*sinB*sinB =((sin^2Acos^2B-cos^2Asin^2B)/sin^2Bcos^2B)*sin^2B =(sin^2Asin^2Bcos^2B-cos^2Asin^2Bsin^2B)/sin^2Bcos^2B =sin^2B-(cos^2Asin^4B/sin^2Bcos^2B) =1-(cos^2A/cos^2B) =1-(n*n) |
