trigonometry

Question

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If A is an angle such that (tan A) + (sec A)=3 enter all possible values of cos A separated by commas.

Guest Mar 9, 2021

amygdaleon305 · Answer 1 · 2021-03-09T02:56:54

Solution -

$tan A + sec A = 3$

${sin A\over cos A} + {1\over cos A} = 3$

$sin A + 1 = 3cos A$

$sin A = 3cos A - 1$

sin²A = 9cos²A - 6cos A + 1

1 - cos²A = 9cos²A - 6cos A +1

10cos²A - 6cos A = 0

5cos A - 3 = 0

cos A = 3/5