SOLUTION: 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

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.

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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.
**
-π/2 < x < π/2
tan(-x) is in quadrant IV where tan<0
tan(π/2-x)is in quadrant I where tan>0
(π/2-x) is the complement of (-x) (reference angles)
tan(x)*tan(complement of x)=1
Therefore, tan(-x)tan(π/2-x)=-1
correct answer is C
Note: This example is for (-π/2 < x < π/2) but it will also be true for the full range of (0-2π)
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