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Solve the following equation for θ where 0≤ θ .
sec (2θ + 5π /7 )=csc (2θ - 27π /14 )

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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.

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