Question 570222
hey how would you solve this problem: select the expression below that is identical to tan(-x)tan(pi/2-x). and here are the choices: A. 1, B. tan squared x, C. -1, D. 2sin squared x, E. 2csc squared x. 
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-&#960;/2 < x < &#960;/2
tan(-x) is in quadrant IV where tan<0
tan(&#960;/2-x)is in quadrant I where tan>0
(&#960;/2-x) is the complement of (-x) (reference angles)
tan(x)*tan(complement of x)=1
Therefore,  tan(-x)tan(&#960;/2-x)=-1
correct answer is C
Note: This example is for (-&#960;/2 < x < &#960;/2) but it will also be true for the full range of (0-2&#960;)