Final answer:
To solve the equation for θ, apply trigonometric identities to simplify the equation and then rearrange it to find the solution.
Step-by-step explanation:
To solve the equation sec(2θ + 5π/7) = csc(2θ - 27π/14) for θ, we can first simplify the equation using trigonometric identities. The reciprocal identities state that secθ = 1/cosθ and cscθ = 1/sinθ. By applying these identities, the equation becomes 1/cos(2θ + 5π/7) = 1/sin(2θ - 27π/14).
To find a solution, we can start by multiplying both sides of the equation by cos(2θ + 5π/7) and sin(2θ - 27π/14). This will eliminate the denominators and simplify the equation.
Next, we can use the Pythagorean identity sin²θ + cos²θ = 1 to continue simplifying and solving the equation for θ.