What is the general solution for sec(w)csc(w)=sqrt(2)sec(w) ?

The general solution for sec(w)csc(w)=sqrt(2)sec(w) is w= pi/4+2pin,w=(3pi)/4+2pin

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sec(w)csc(w)=sqrt(2)sec(w)

sec (w) csc (w) = 2 sec (w)

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

Solution steps

sec (w) csc (w) = 2 sec (w)

Subtract

2 sec (w)

from both sides

sec (w) csc (w) - 2 sec (w) = 0

Factor

sec (w) csc (w) - 2 sec (w) : sec (w) (csc (w) - 2)

sec (w) (csc (w) - 2) = 0

Solving each part separately

sec (w) = 0 or csc (w) - 2 = 0

sec (w) = 0 :

No Solution

csc (w) - 2 = 0 : w = \frac{π}{4} + 2 πn, w = \frac{3 π}{4} + 2 πn

Combine all the solutions

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

- 2 sin (x) - cos (2 x) \cdot 2 = 0

- 2 cos (B) + 4 = cos (B) + 6

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

csc^{3} (x) + csc^{2} (x) = 2 csc (x) + 2

cot^{2} (x) sin (x) = cot^{2} (x)

What is the general solution for sec(w)csc(w)=sqrt(2)sec(w) ?
The general solution for sec(w)csc(w)=sqrt(2)sec(w) is w= pi/4+2pin,w=(3pi)/4+2pin