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How to simplify these two expressions?

 Feb 19, 2018
edited by Guest  Feb 19, 2018
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1.   (csc^2(x) - cot^2(x)) / (sin(-x)cot(x)

      

      Remember that  1 + cot^2 (x)  = csc^2 (x)

      So  csc^2 (x) - cot^2(x)  =  1

 

      Also   sin (-x)  =   - sin (x)

 

So  we have

 

1 / [ - sin (x) (cos (x)  / sin (x) ]  =

 

1 / (-cos (x) )  =    -  sec (x)

 

 

2.  sin ^2 (x)cos^2(x)  - cos^2(x)  =

 

(1  - cos^2(x) ) (cos^2 (x) ) -  cos^2(x)

 

cos^2(x) - cos^4 (x)   - cos^2(x)

 

-cos^4(x)

 

 

cool cool cool

 Feb 19, 2018

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