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In triangle ABC, if angle A satisfies 5 cos A + 3 = 0, then the values of sin A and tan A are the roots of which quadratic equation?

1. 15x² − 8x − 16 = 0
2. 15x² − 8√2x + 16 = 0
3. 15x² − 8x + 16 = 0
4. 15x² + 8x − 16 = 0

Correct answer: 15x² + 8x − 16 = 0

Solution

From 5cosA+3=0, cosA=-3/5; since A is a triangle angle it is obtuse, sinA=4/5 and tanA=-4/3. Sum of roots = -8/15, product = -16/15, giving 15x^2+8x-16=0.

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