How do you prove #1/(1+sin(theta)) + 1/(1-sin(theta)) = 2sec^2(theta)#?

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Answer 1 · 2016-04-17T00:31:48

See below

LHS =left hand side, RHS =right hand side

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

#=(1-sin theta +1+sin theta )/((1+sin theta)(1-sin theta)) #->Common Denominator

#=(1-cancelsin theta +1+cancelsin theta )/((1+sin theta)(1-sin theta)) #

#=2/(1-sin^2x)#

#=2/cos^2x#

#=2*1/cos^2x#

#=2sec^2x#

#=RHS #