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find all solutions of the equation in the interval [0,2pi ) csc2x-sqrt (2)=0 write your answer in radians in terms of pi if there is

Question

Find all solutions of the equation in the interval [0,2pi ) csc2x-sqrt (2)=0 Write your answer in radians in terms of pi If there is more than one solution , separate them with commas.

Solution

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Resposta

To find all solutions of the equation in the interval , we first solve the equation for : Since , we can rewrite the equation as: Taking the reciprocal of both sides, we get: Simplifying further, we have: The solutions for in the interval are: Dividing each of these by 2, we get: Therefore, the solutions to the equation in the interval are: