VESTIGE

10. (a) (b) (C) Some formulae for compound angles (e) sin(A+B).sin(A-B) = sin'A-sin'B= cos'B-cos'A cos(A+B).cos(A-B) = cos'A-sin'B = cos'B- sin'A sin(A+B+C) = sin A. cos B.cosC + cos A.sin B.cos C + cos A. cos B. sinC-sinA. sinB.sinC = cos A. cos B. cos C (tan AttanB + tan C- tan A. tan B. tanC) (d) cos(A+B+C) = cosA.cosB.cosC - sinA.sinB.cosC- sinA.cosB.sinC-cosA.sinB.sinC =coSA.cosB.cosC(1-tanA.tanB-tanB.tanC-tanC.tanA) tan(A+B+C) tanA+tanB+tanC-tanA.tanB.tanC 1- tanA.tanB- tanB.tanC -tanC.tanA 0 cot(A+B+C) cotA.cosB.cotC- cotA -cotB-cotC cotA.cotB+cotB.cotC+cotC.cotA -1