Step 1a

Multiply the entire equation by 12 \$("the least common denominator of" 1/4 "and" 1/3)\$ to eliminate the fractions.

\$12(1/4(secθ -2)) = 12(1/3(secθ -1))\$

\$3(secθ - 2) = 4(secθ - 1)\$

Explanation: Multiply the provided trigonometric equation by 12 and then simplify it.

Step 1b

Now isolate secθ on one side of the equal sign.

3secθ - 6 = 4secθ - 4

- 6 + 4 = 4secθ - 3secθ

- 2 = secθ

The equality of a statement is preserved if you take the reciprocal of both sides of the equation. Recall that secant is defined as the reciprocal of cosine.
\$- 1/2 = 1/(secθ)\$

\$ - 1/2 = cosθ \$

Explanation: To find the secant value of θ, then determine the cosine value through its reciprocal.

Step 1c

The unit circle has a cosine of \$-1/2\$ at \$θ = (2pi)/3\$ and \$θ = (4pi)/3\$, with coterminal angles by adding multiples of \$(2pi)\$.
\$θ = (2pi)/3 + 2k(pi)\$ , \$θ = (4pi)/3 + 2k(pi)\$ , such that k is an integer.

Explanation: Calculate θ values by adding multiples of 2π, where k is an integer, to achieve accurate results.