1+sinx/cosx + cosx/ 1+sinx = 2secx
cosX / (1+ sinX)
multiply this term with (1-sinX) in Numerator and denominator
cosX *(1-sinX)/ (1+sinX )(1-sinX)
= cosX*(1-sinX) / (1-sin^2X)
= cosX*(1-sinx) / cos^2 X ...... acc. to identity sin^2X + cos^2X = 1 or 1 - sin^2X = cos^2X
now cosX canel out from numerator and denominator
= (1-sinX) / cosX
now see the problemm
(1 + sinX)/ cosX + cosX(1-sinX)
put the value of cosX(1-sinX) which is calculated above
(1+sinX) / cosX + (1-sinX)/cosX
Take LCM cosX
=( 1+sinX + 1- sinX)/ cosX
= 2 / cosX
and we know that 1/cosX = secX
= 2secX which is equal to Right Hand Side
so identity estaablished
This was very helpful, thank you!
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