What is the general solution for 2tan(x)+sec^2(x)=0,-90<x<90 ?

The general solution for 2tan(x)+sec^2(x)=0,-90<x<90 is x=-45

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2tan(x)+sec^2(x)=0,-90<x<90

2 tan (x) + sec^{2} (x) = 0, - 9 0^{\circ} < x < 9 0^{\circ}

x = - 4 5^{\circ}

Solution steps

2 tan (x) + sec^{2} (x) = 0, - 9 0^{\circ} < x < 9 0^{\circ}

Rewrite using trig identities

1 + tan^{2} (x) + 2 tan (x) = 0

Solve by substitution

tan (x) = - 1

tan (x) = - 1, - 9 0^{\circ} < x < 9 0^{\circ} : x = - 4 5^{\circ}

Combine all the solutions

x = - 4 5^{\circ}

tan (6 0^{\circ} - θ) = \frac{1}{3}

x, 1 - 2 cos (x) = 0

0 = 1 + sin (θ)

2 cos (2 x) - cos (x) - 1 = 0

tan (x) \cdot tan (2 x) = 1

What is the general solution for 2tan(x)+sec^2(x)=0,-90<x<90 ?
The general solution for 2tan(x)+sec^2(x)=0,-90<x<90 is x=-45