Prove each of the following identities (a) sec x + tan x =cos x/1 − sin x (b) tan^2 x/tan^2 x + 1= sin^2 x?

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Answer 1 · 2018-07-16T10:38:31

a)

#LHS=sec x + tan x#

#=1/cosx + sinx/cosx#

#=((1 + sinx)cosx)/cos^2x#

#=((1 + sinx)cosx)/(1-sin^2x)#

#=((1 + sinx)cosx)/((1-sinx)(1+sinx))#

#=cos x/(1 − sin x)=RHS#

(b) #LHS=tan^2 x/(tan^2 x + 1)#

#=tan^2 x/sec^2 x#

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

#= sin^2 x=RHS#