Final answer:
The identity 'cot t tan t = 1/ tan t' has a typo. Upon verification using basic trigonometry, the correct identity is 'cot t tan t = 1,' as cot t is the reciprocal of tan t, and when multiplied together, they yield 1.
Step-by-step explanation:
To verify the identity cot t tan t = 1/ tan t, we can utilize the basic properties of trigonometry. The cotangent function cot t is defined as the reciprocal of the tangent function, which means cot t = 1/ tan t. Therefore, if we multiply cot t by tan t, we get:
cot t × tan t = (1/ tan t) × tan t
Since tan t in the numerator and denominator cancel each other out, we are left with:
cot t × tan t = 1
The equation states that cot t tan t should equal 1/ tan t. This seems incorrect because we just verified that cot t tan t = 1, not 1/ tan t. Therefore, the student's version of the identity contains a typo or misunderstanding. The correct identity is cot t tan t = 1, not 1/ tan t.