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If 5 tan A = 4 then find the value of (5 sin A - 3 cos A)/ (5 sin A + 3 cos A) |
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Answer» 5 tan A = 4 Tan A = 4/5 Tan A = P/B = 4/5 H = √P2 + B2 = √42 + 52 = √16+25 = √41 Sin A = P/H = 4/√41 Cos A = B/H = 5/√41 Substituting the value now, = (5 sin A - 3 cos A)/ (5 sin A + 3 cos A) = (5 x 4/√41 - 3 x 5/√41) / (5 x 4/√41 + 3 x 5/√41 ) = ( 20/√41 - 15/√41 ) / ( 20/√41 + 15/√41 ) = ( (20-15)/√41) / ((20+15)/√41) = 5/√41 / 35/√41 = 5/√41 x √41/35 = 1/7 |
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