Question

question the expression 6 + 6 cot²x is equivalent to answer 6 sin²x - 6 sin²x 6 tan²x - 6 tan²x 6 sec²x - 6 sec²x 6 cos²x - 6 cos²x 6 csc²x - 6 csc²x 6 cot²x - 6 cot²x - 6

Explanation:

Step1: Use the Pythagorean identity \(1+\cot^{2}x=\csc^{2}x\)

Given the expression \(6 + 6\cot^{2}x\), factor out the common factor of 6: \(6(1+\cot^{2}x)\)

Step2: Substitute the identity

Since \(1+\cot^{2}x=\csc^{2}x\), then \(6(1 + \cot^{2}x)=6\csc^{2}x\)

Answer:

\(6\csc^{2}x\)