Math CentralQuandaries & Queries


Question from sumayya, a student:
prove that sin A (1+tan A)+cos A (1+cot A)= sec A+ cosec A
  1. Write everything in terms of sines and cosines.

    (eg, tan A -> sinA/cosA, sec A = 1/cosA, etc)

  2. Multiply both sides through by whatever is necessary to get an equivalent equation with no fractional expressions

  3. Regroup terms so that you can use the Pythagorean identity
    to simplify

    eg, sin3 A + cos2A sin A = (sin2 A + cos2 A) sin A
    = 1 sin A
    = sin(A)

Good Hunting!


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