What is the general solution for sec^2(x)cos(x)=cos(x),0<x<360 ?

The general solution for sec^2(x)cos(x)=cos(x),0<x<360 is x=180

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sec^2(x)cos(x)=cos(x),0<x<360

sec^{2} (x) cos (x) = cos (x), 0^{\circ} < x < 36 0^{\circ}

x = 18 0^{\circ}

Solution steps

sec^{2} (x) cos (x) = cos (x), 0^{\circ} < x < 36 0^{\circ}

Subtract

cos (x)

from both sides

sec^{2} (x) cos (x) - cos (x) = 0

Factor

sec^{2} (x) cos (x) - cos (x) : cos (x) (sec (x) + 1) (sec (x) - 1)

cos (x) (sec (x) + 1) (sec (x) - 1) = 0

Solving each part separately

cos (x) = 0 or sec (x) + 1 = 0 or sec (x) - 1 = 0

cos (x) = 0, 0 < x < 36 0^{\circ} : x = 9 0^{\circ}, x = 27 0^{\circ}

sec (x) + 1 = 0, 0 < x < 36 0^{\circ} : x = 18 0^{\circ}

sec (x) - 1 = 0, 0 < x < 36 0^{\circ} :

No Solution

Combine all the solutions

x = 9 0^{\circ}, x = 27 0^{\circ}, x = 18 0^{\circ}

Since the equation is undefined for:

9 0^{\circ}, 27 0^{\circ}

x = 18 0^{\circ}

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csc (x) + cot (x) = 0

cos^{2} (θ) - sin^{2} (θ) = 0

7 = 4 sin (\frac{π}{2} (x - 2)) + 5

3 tan^{4} (x) - 3 tan^{3} (x) - tan^{2} (x) + tan (x) = 0

What is the general solution for sec^2(x)cos(x)=cos(x),0<x<360 ?
The general solution for sec^2(x)cos(x)=cos(x),0<x<360 is x=180