What is the general solution for sec(x)*cot(x)-2cot(x)+sec(x)=2 ?

The general solution for sec(x)*cot(x)-2cot(x)+sec(x)=2 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(3pi)/4+pin

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sec(x)*cot(x)-2cot(x)+sec(x)=2

sec (x) \cdot cot (x) - 2 cot (x) + sec (x) = 2

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{3 π}{4} + πn

Solution steps

sec (x) cot (x) - 2 cot (x) + sec (x) = 2

Subtract

2

from both sides

sec (x) cot (x) - 2 cot (x) + sec (x) - 2 = 0

Factor

sec (x) cot (x) - 2 cot (x) + sec (x) - 2 : (sec (x) - 2) (cot (x) + 1)

(sec (x) - 2) (cot (x) + 1) = 0

Solving each part separately

sec (x) - 2 = 0 or cot (x) + 1 = 0

sec (x) - 2 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cot (x) + 1 = 0 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{3 π}{4} + πn

3 sin^{2} (x) - 10 sin (x) - 8 = 0

2 \cdot 9.8 \cdot L (1 - cos (θ)) = 0.018

cos (7 x) = sin (4 x + 2)

12 cos (β) - 5 sin (β) = 4.7

cos (x) = \frac{8}{3}

What is the general solution for sec(x)*cot(x)-2cot(x)+sec(x)=2 ?
The general solution for sec(x)*cot(x)-2cot(x)+sec(x)=2 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(3pi)/4+pin