Question #5121f

1 Answer
Feb 8, 2018

#LHS=( sin theta + cos theta )/( sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta ) #

#=(( sin theta + cos theta )^2+( sin theta - cos theta )^2) /( ( sin theta - cos theta )( sin theta + cos theta )) #

#=(2( sin^2 theta + cos^2 theta )) /( ( sin ^2theta - cos ^2theta ) #

#=2/( sin ^2theta - cos ^2theta ) #

#=(2/cos^2theta)/( sin ^2theta/cos^2theta - cos ^2theta/ cos^2theta) #

#= (2 sec^2theta)/ (tan^2 theta - 1)=RHS#