Complete the proof of the identity by choosing the Rule that justifies each step.=sen2x+1cot2x1To see a detailed description of a Rule, select the More Information Button to the right of the Rule.Statement Rulesen2x+1cot2x =sen2xcsc2x Rule ?=sen2x1sen2x Rule ?=1 Rule ?
Question
Complete the proof of the identity by choosing the Rule that justifies each step.=sen2x+1cot2x1To see a detailed description of a Rule, select the More Information Button to the right of the Rule.Statement Rulesen2x+1cot2x =sen2xcsc2x Rule ?=sen2x1sen2x Rule ?=1 Rule ?
Solution
The proof of the identity sen2x + 1cot2x = 1 can be justified by the following rules:
Statement: sen2x + 1cot2x Rule: This is the initial statement.
Statement: = sen2x * csc2x Rule: This step is justified by the identity cotx = 1/cscx. Therefore, 1cot2x can be rewritten as csc2x.
Statement: = sen2x * 1/sen2x Rule: This step is justified by the identity cscx = 1/senx. Therefore, csc2x can be rewritten as 1/sen2x.
Statement: = 1 Rule: This step is justified by the rule that any number divided by itself equals 1. Therefore, sen2x * 1/sen2x simplifies to 1.
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