SOLUTION: Given: sin(x) - cos(x) = 1/(5^1/2) find the value of tan(x) + cot(x) + cos(2x)

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Question 1199966: Given: sin(x) - cos(x) = 1/(5^1/2) find the value of tan(x) + cot(x) + cos(2x)
Answer by ikleyn(52816)   (Show Source): You can put this solution on YOUR website!
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Given: sin(x) - cos(x) = 1/(5^1/2) find the value of tan(x) + cot(x) + cos(2x)
~~~~~~~~~~~~~~~~~ 

The given equality  sin(x) - cos(x) =   implies after squaring


    sin^2(x) - 2sin(x)*cos(x) + cos^2(x) = 

    1 - sin(2x) = 

    1 -  = sin(2x)

    sin(2x) = .      (1)


The value of  tan(x) + cot(x) + cos(2x) is

       +  + cos(2x) = 

    =  + cos(2x) = 

    =  + cos(2x).


Substitute here sin(2x) =   and  cos(2x) =  =  = ,  based on (1).  You will get

    tan(x) + cot(x) + cos(2x) =  +  =  +  =  +  = 

                              =  =  =  = 3.1.    ANSWER


ANSWER.  If  sin(x) - cos(x) =   then  tan(x) + cot(x) + cos(2x) =  = 3.1.

Solved.



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