Which identity is not used in the proof of the identity 1+cot^2 theta =csc^2 theta

*urgent*
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Imogene invested $8,000 in a bank account that pays 8 percent simple interest at the end of each year. her friend invested the same amount in stocks where the growth of the investment is represented as 2,000 times the square root of 2 less than the time lapsed in years. if y1 and y2 represent the amount earned in dollars and t is the time lapsed in years, which system of equations correctly represents the situation?

Given that abcd is a rhombus, what is the value of x?

For the inequality |c| < |d| to be true, which of the following must be true?