What is the general solution for cos^2(x)sec(x)=1 ?

The general solution for cos^2(x)sec(x)=1 is x=2pin

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cos^2(x)sec(x)=1

cos^{2} (x) sec (x) = 1

x = 2 πn

Degrees

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

Solution steps

cos^{2} (x) sec (x) = 1

Subtract

1

from both sides

cos^{2} (x) sec (x) - 1 = 0

Rewrite using trig identities

- 1 + cos^{2} (x) sec (x)

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= - 1 + cos^{2} (x) \frac{1}{cos ( x )}

cos^{2} (x) \frac{1}{cos ( x )} = cos (x)

cos^{2} (x) \frac{1}{cos ( x )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot cos ^{2} ( x )}{cos ( x )}

Multiply:

1 \cdot cos^{2} (x) = cos^{2} (x)

= \frac{cos ^{2} ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= cos (x)

= - 1 + cos (x)

- 1 + cos (x) = 0

Move

1

to the right side

- 1 + cos (x) = 0

Add

1

to both sides

- 1 + cos (x) + 1 = 0 + 1

Simplify

cos (x) = 1

cos (x) = 1

General solutions for

cos (x) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

What is the general solution for cos^2(x)sec(x)=1 ?
The general solution for cos^2(x)sec(x)=1 is x=2pin