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If y = tanX +SinX then proov that y" = cosX/(1-sinX)^2

If y = tanX +SinX then proov that y" = cosX/(1-sinX)^2

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago
Dear student
 
dwr to x
            y'= Sec^2 x + Sec x tan x = y Sec x
            y” = y sec x tan x + y'sec x
                =  sec x ( ytanx + y')
                 = sec x ( tan^2x + sec x tan x + sec x tan x + sec^2 x)
                 = sec x ( sec x + tan x )^2
                 = (1/cos x)( 1+ Sin x/Cosx )^2
                 = (1+Sin x)^2/ Cos^3 x
                 = (1+Sin x)^2. (1-Sin x)^2/Cos^3 x (1-Sin x)^2
                 = Cos^4 x / Cos^3 x (1-Sin x)^2
                 = Cos x / (1-Sin x)^2.    

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