What is the general solution for csc(x)=sec(41) ?

The general solution for csc(x)=sec(41) is x=0.85521…+360n,x=180-0.85521…+360n

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csc(x)=sec(41)

csc (x) = sec (4 1^{\circ})

x = 0.85521 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.85521 \dots + 36 0^{\circ} n

Radians

x = 0.85521 \dots + 2 πn, x = π - 0.85521 \dots + 2 πn

Solution steps

csc (x) = sec (4 1^{\circ})

Apply trig inverse properties

csc (x) = sec (4 1^{\circ})

General solutions for

csc (x) = sec (4 1^{\circ})

csc (x) = a \Rightarrow x = arccsc (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arccsc (a) + 36 0^{\circ} n

x = arccsc (sec (4 1^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arccsc (sec (4 1^{\circ})) + 36 0^{\circ} n

x = arccsc (sec (4 1^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arccsc (sec (4 1^{\circ})) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.85521 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.85521 \dots + 36 0^{\circ} n

sin (x) - sin (3 x) = 0

2 sin^{2} (θ) - 5 cos (θ) + 1 = 0

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

5 sin (x) - 4 = 2 cos (2 x)

csc (x) + cot (x) = 0

What is the general solution for csc(x)=sec(41) ?
The general solution for csc(x)=sec(41) is x=0.85521…+360n,x=180-0.85521…+360n