Trigonometric Equations 2

Find all the angles between 0° and 360° which satisfy the equation sec y(1 + tan y) = 6 cosec y.

Solution: y= 63.4, 243.4, 108.4, 288.4

1/cosy (1 + tany) = 6(1/siny)

1 + tany = 6 cosy/siny

1 + tany = 6 coty

tany + tan2y = 6

tany + tan2y – 6 = 0

tany = 2                 or                tany = -3

1st and 3rd quadrant                2nd and 4th quadrant

y = 63.435, 243.43                    y= 108.43, 288.43

y = 63.4, 243.4                          y = 108.4, 288.4

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