Answers

1. Answer:

   135 and 315degrees

   Step-by-step explanation:

   Given the expression

   4tan²θ+tanθ=−4tanθ−1

   Equate to zero

   4tan²θ+tanθ+4tanθ+1 = 0

   4tan²θ+5tanθ+1 = 0

   Let x = tanθ

   4x²+5x+1 = 0

   Factorize;

   4x²+4x+x+1 = 0

   4x(x+1)+1(x+1) = 0

   4x+1 = 0 and x+1 = 0

   4x = -1 and x = -1

   x = -1/4 and -1

   Since x = tanθ

   -1 =tanθ

   θ = arctan(-1)

   θ = -45degrees

   Since tan is negative in the 2nd and fourth quadrant;

   In the second quadrant

   θ = 180 – 45 = 135degrees

   In the fourth quadrant;

   θ = 360 – 45 = 315degrees

   Hence the required angles are 135 and 315degrees

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