What is the general solution for csc(42)=sec(x) ?

The general solution for csc(42)=sec(x) is x=0.83775…+360n,x=360-0.83775…+360n

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csc(42)=sec(x)

csc (4 2^{\circ}) = sec (x)

x = 0.83775 \dots + 36 0^{\circ} n, x = 36 0^{\circ} - 0.83775 \dots + 36 0^{\circ} n

Radians

x = 0.83775 \dots + 2 πn, x = 2 π - 0.83775 \dots + 2 πn

Solution steps

csc (4 2^{\circ}) = sec (x)

Switch sides

sec (x) = csc (4 2^{\circ})

Apply trig inverse properties

sec (x) = csc (4 2^{\circ})

General solutions for

sec (x) = csc (4 2^{\circ})

sec (x) = a \Rightarrow x = arcsec (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (a) + 36 0^{\circ} n

x = arcsec (csc (4 2^{\circ})) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (csc (4 2^{\circ})) + 36 0^{\circ} n

x = arcsec (csc (4 2^{\circ})) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (csc (4 2^{\circ})) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.83775 \dots + 36 0^{\circ} n, x = 36 0^{\circ} - 0.83775 \dots + 36 0^{\circ} n

x, 0 = cos (x) + 1 + sin (x)

5 sin (\frac{π}{4} x) = 4

1 - sec^{2} (θ) = tan^{2} (θ)

6 tan^{2} (x) = 5 sec (x)

x, cos^{2} (x) = 0.5

What is the general solution for csc(42)=sec(x) ?
The general solution for csc(42)=sec(x) is x=0.83775…+360n,x=360-0.83775…+360n