What is the general solution for sec(x+45)=1 ?

The general solution for sec(x+45)=1 is x=360n-45

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sec(x+45)=1

sec (x + 4 5^{\circ}) = 1

x = 36 0^{\circ} n - 4 5^{\circ}

Radians

x = - \frac{π}{4} + 2 πn

Solution steps

sec (x + 4 5^{\circ}) = 1

General solutions for

sec (x + 4 5^{\circ}) = 1

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x + 4 5^{\circ} = 0 + 36 0^{\circ} n

x + 4 5^{\circ} = 0 + 36 0^{\circ} n

Solve

x + 4 5^{\circ} = 0 + 36 0^{\circ} n : x = 36 0^{\circ} n - 4 5^{\circ}

x + 4 5^{\circ} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

x + 4 5^{\circ} = 36 0^{\circ} n

Move

4 5^{\circ}

to the right side

x + 4 5^{\circ} = 36 0^{\circ} n

Subtract

4 5^{\circ}

from both sides

x + 4 5^{\circ} - 4 5^{\circ} = 36 0^{\circ} n - 4 5^{\circ}

Simplify

x = 36 0^{\circ} n - 4 5^{\circ}

x = 36 0^{\circ} n - 4 5^{\circ}

x = 36 0^{\circ} n - 4 5^{\circ}

117.72 sin (θ) - 35.316 cos (θ) - 12.5 = 0

- 2 sin (θ) = 0

sec^{3} (x) = - 1

\frac{1}{cot ^{2} ( x )} + 3 tan (x) = 0

tan (x) = 0.23

What is the general solution for sec(x+45)=1 ?
The general solution for sec(x+45)=1 is x=360n-45