1/ (secx - tanx) -1/cosx = 1/cosx - 1/(secx +tanx)

Asked by Sthitaprajna Mishra | 7th Aug, 2014, 06:45: AM

Expert Answer:

C o n s i d e r space t h e space l e f t space h a n d space s i d e space o f space t h e space e q u a t i o n : fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator open parentheses s e c x plus tan x close parentheses over denominator open parentheses s e c x minus tan x close parentheses open parentheses s e c x plus tan x close parentheses end fraction minus fraction numerator 1 over denominator cos x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator open parentheses s e c x plus tan x close parentheses over denominator s e c squared x minus tan squared x end fraction minus fraction numerator 1 over denominator cos x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator open parentheses s e c x plus tan x close parentheses over denominator 1 end fraction minus fraction numerator 1 over denominator cos x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals s e c x plus tan x minus fraction numerator 1 over denominator cos x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction plus tan x minus fraction numerator 1 over denominator cos x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction plus fraction numerator cos x cross times tan x minus 1 over denominator cos x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction minus fraction numerator 1 minus cos x cross times tan x over denominator cos x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction minus fraction numerator 1 minus sin x over denominator cos x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction minus fraction numerator 1 minus sin x over denominator cos x end fraction cross times fraction numerator 1 plus sin x over denominator 1 plus sin x end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction minus fraction numerator 1 minus sin squared x over denominator cos x open parentheses 1 plus sin x close parentheses end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction minus fraction numerator cos squared x over denominator cos x open parentheses 1 plus sin x close parentheses end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction minus fraction numerator cos x over denominator open parentheses 1 plus sin x close parentheses end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction minus fraction numerator 1 over denominator open parentheses begin display style fraction numerator 1 over denominator cos x end fraction end style plus begin display style fraction numerator sin x over denominator cos x end fraction end style close parentheses end fraction rightwards double arrow fraction numerator 1 over denominator s e c x minus tan x end fraction minus fraction numerator 1 over denominator cos x end fraction equals fraction numerator 1 over denominator cos x end fraction minus fraction numerator 1 over denominator open parentheses s e c x plus begin display style tan x end style close parentheses end fraction

Answered by Vimala Ramamurthy | 7th Aug, 2014, 09:25: AM