A trig identity - Math Central

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Quandaries & Queries

Question from sumayya, a student:
prove that sin A (1+tan A)+cos A (1+cot A)= sec A+ cosec A

Write everything in terms of sines and cosines.

(eg, tan A -> sinA/cosA, sec A = 1/cosA, etc)
Multiply both sides through by whatever is necessary to get an equivalent equation with no fractional expressions
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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