Evaluate the following expression.
4 tan t cot t

A)3
B)5
C)4
D)2
E)6

Name: Evaluate the following expression. 4 tan t cot t A)3 B)5 C)4 D)2 E)6
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Question

Evaluate the following expression. ​
4 tan t cot t
​
A)3
B)5
C)4
D)2
E)6

Quizplus · Accepted Answer

We know that cot t = 1/tan t. 
So, 4 tan t cot t = 4 tan t / (1/tan t) = 4 tan^2 t 
Now we know that 1 + tan^2 t = sec^2 t 
So, tan^2 t = sec^2 t - 1 
Substituting in the formula, we get 
4 (sec^2 t - 1) 
= 4 sec^2 t - 4 
= 4 (sec^2 t - 1) + 4 
= 4 tan^2 t + 4 
= 4*1 + 4 = 8 
Therefore, 4 tan t cot t = 8/2 = 4, which is option C.

Evaluate the Following Expression. ​

Evaluate the Following Expression.