if sec tita = x+1/4x
sec tita +tan tita =2x or 1/2x

Asked by sapnabhoopendra | 6th Sep, 2016, 07:28: PM

Expert Answer:

begin mathsize 12px style secθ space equals space straight x plus fraction numerator 1 over denominator 4 straight x end fraction
To space prove colon space sec straight theta space plus space tanθ space equals space 2 straight x space or space fraction numerator 1 over denominator 2 straight x end fraction
We space know space that comma space 1 space plus space tan squared straight theta equals sec squared straight theta
rightwards double arrow space tan squared straight theta equals open parentheses straight x plus fraction numerator 1 over denominator 4 straight x end fraction close parentheses squared minus 1
rightwards double arrow space tan squared straight theta equals straight x squared plus fraction numerator 1 over denominator 16 straight x end fraction squared plus 1 half minus 1
rightwards double arrow space tan squared straight theta equals open parentheses straight x minus fraction numerator 1 over denominator 4 straight x end fraction close parentheses squared
rightwards double arrow space tanθ equals straight x minus fraction numerator 1 over denominator 4 straight x end fraction space space space space space space or space space space minus open parentheses straight x minus fraction numerator 1 over denominator 4 straight x end fraction close parentheses
When space space tanθ equals straight x minus fraction numerator 1 over denominator 4 straight x end fraction comma space we space get comma space secθ space plus space tanθ space equals space straight x plus fraction numerator 1 over denominator 4 straight x end fraction plus straight x minus fraction numerator 1 over denominator 4 straight x end fraction equals 2 straight x
When space space tanθ equals negative open parentheses straight x minus fraction numerator 1 over denominator 4 straight x end fraction close parentheses comma space we space get comma space secθ space plus space tanθ space equals space straight x plus fraction numerator 1 over denominator 4 straight x end fraction minus open parentheses straight x minus fraction numerator 1 over denominator 4 straight x end fraction close parentheses equals straight x plus fraction numerator 1 over denominator 4 straight x end fraction minus straight x plus fraction numerator 1 over denominator 4 straight x end fraction equals fraction numerator 2 over denominator 4 straight x end fraction equals fraction numerator 1 over denominator 2 straight x end fraction
Hence space proved. end style

Answered by Rebecca Fernandes | 6th Sep, 2016, 09:20: PM