What is the general solution for sec^2(x)cot(x)=4 ?

The general solution for sec^2(x)cot(x)=4 is x= pi/(12)+pin,x=(5pi)/(12)+pin

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sec^2(x)cot(x)=4

sec^{2} (x) cot (x) = 4

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

Solution steps

sec^{2} (x) cot (x) = 4

Subtract

4

from both sides

sec^{2} (x) cot (x) - 4 = 0

Express with sin, cos

\frac{1 - 4 cos ( x ) sin ( x )}{cos ( x ) sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 - 4 cos (x) sin (x) = 0

Rewrite using trig identities

1 - 4 \cdot \frac{sin ( 2 x )}{2} = 0

4 \cdot \frac{sin ( 2 x )}{2} = 2 sin (2 x)

1 - 2 sin (2 x) = 0

Move

1

to the right side

- 2 sin (2 x) = - 1

Divide both sides by

- 2

sin (2 x) = \frac{1}{2}

General solutions for

sin (2 x) = \frac{1}{2}

2 x = \frac{π}{6} + 2 πn, 2 x = \frac{5 π}{6} + 2 πn

Solve

2 x = \frac{π}{6} + 2 πn : x = \frac{π}{12} + πn

Solve

2 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

1 = 4 cos (2 θ)

209 cos (4 7^{\circ}) = 150 cos (θ)

7 - 5 cos (x) = 10, 7 - 5 cos (x) = 10

cos (4 x) = cos (x)

- 4 cos (2 θ) - 19 = - 26 cos (θ), 0 \leq θ < 36 0^{\circ}

What is the general solution for sec^2(x)cot(x)=4 ?
The general solution for sec^2(x)cot(x)=4 is x= pi/(12)+pin,x=(5pi)/(12)+pin