What is the general solution for sec(θ)cos(θ)tan(θ)=1 ?

The general solution for sec(θ)cos(θ)tan(θ)=1 is θ= pi/4+pin

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sec(θ)cos(θ)tan(θ)=1

sec (θ) cos (θ) tan (θ) = 1

θ = \frac{π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

sec (θ) cos (θ) tan (θ) = 1

Rewrite using trig identities

sec (θ) cos (θ) tan (θ)

sec (θ) cos (θ) = 1

sec (θ) cos (θ)

Express with sin, cos

sec (θ) cos (θ)

Use the basic trigonometric identity:

sec (θ) = \frac{1}{cos ( θ )}

= \frac{1}{cos ( θ )} cos (θ)

\frac{1}{cos ( θ )} cos (θ) = 1

\frac{1}{cos ( θ )} cos (θ)

Multiply fractions:

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

= \frac{1 cos ( θ )}{cos ( θ )}

Cancel the common factor:

cos (θ)

= 1

= 1

= 1 \cdot tan (θ)

1 \cdot tan (θ) = 1

Multiply:

1 \cdot tan (θ) = tan (θ)

tan (θ) = 1

General solutions for

tan (θ) = 1

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

cos^{3} (x) - 3 cos (x) = 3 cos (x) sin (x)

sin (x) = 0.88

tan (b) = 1

5 cos^{2} (θ) - 1 = cos^{2} (θ)

cos (x) = \frac{2}{9}

What is the general solution for sec(θ)cos(θ)tan(θ)=1 ?
The general solution for sec(θ)cos(θ)tan(θ)=1 is θ= pi/4+pin