Prove that (cosA/1+sinA)+(1+sinA/cosA)=2secA?

1 Answer
Jane
Mar 2, 2018

Given,

# cos A/(1+sin A) + (1+sin A)/cos A#

#=((cos A*cos A) +(1+sin A)(1+ sin A))/(cos A(1+ sin A))#

#= (cos^2 A +1 + 2sin A + sin^2 A)/(cos A(1+sin A)#

#=( 2 + 2 sin A)/(cos A(1+sin A))# (as, #cos ^2 A + sin^2 A=1#)

#= (2(1+sin A)) /(cos A(1+sin A))#

#= 2/cos A = 2sec A#

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