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How to solve this trigonometry problem?

+4 votes

I need to prove that the following is true by using trigonometric identities to get one side of the equation to match the other 
*I can only rearrange ONE SIDE of the equation to prove this:
(csc(x) + cot(x)) / (sin(x) + tan(x)) =cot(x)*csc(x)

asked Jan 16, 2013 in TRIGONOMETRY by linda Scholar

1 Answer

+4 votes

1. (cscx + cotx)/ sinx + tanx =cot x *cscx

   = ( 1 /sinx +cosx /sinx) /(sinx +sinx /cosx)

                                                       (since csc =1 /sinx ,cotx =cosx /sinx , tanx = sinx /cosx )

  =( (1 +cosx)/sinx )/ (sinx*cosx +sinx )/cosx

divided change to multipltication

 =( (1 +cosx)/sinx )*cosx/(sinx*cosx +sinx )

take out common sinx term

=(1 +cosx)/sinx )*cosx/ sinx(cosx + 1)

cancel common (1 +cosx ) terms

= (1/sinx)*(cosx/sinx)

=cscx*cotx     (a*b=b*a)

=cotx*cscx

the solutions to prove. (cscx + cotx)/ sinx + tanx =cot x *cscx

answered Jan 18, 2013 by krish Pupil

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