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Answer 1 · 2017-08-19T17:37:39

Given

#sectheta+tantheta=x.....[1]#

Now

#sectheta-tantheta=( sec^2theta-tan^2theta ) /(sectheta+tantheta)#

#=>sectheta-tantheta=1 /(sectheta+tantheta)#

#=>sectheta-tantheta=1 /x....[2]#

Adding [1] and [2] we get

#2sectheta=(x+1/x)... .[3]#

Subtracting [2] from [1] we get

#2tantheta=(x-1/x)......[4]#

#=>tantheta=1/2(x-1/x)#

Duviding [4] by [3] we get

#sintheta=(x-1/x)/(x+1/x)=(x^2-1)/(x^2+1)#