To prove #(1+sin theta -cos theta)/(1+sin theta + cos theta) = tan (theta / 2)# ?

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Answer 1 · 2018-05-11T02:13:05

#LHS=(1+sin theta -cos theta)/(1+sin theta + cos theta) #

#=(sintheta(1+sin theta -cos theta))/(sintheta(1+sin theta + cos theta)) #

#=(sintheta(1+sin theta -cos theta))/(sintheta+sin^2theta + sinthetacos theta) #

#=(sintheta(1+sin theta -cos theta))/(sintheta(1+costheta)+(1-cos^2theta) #

#=(sintheta(1+sin theta -cos theta))/((1+costheta)(sintheta+1-costheta) )#

#=sintheta/((1+costheta)#

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

#= tan (theta / 2)=RHS#