Question

Suppose y= (x/sqrt(a^2-1) ) - (2/sqrt(a^2-1)) * tan^-1(sinx/a+sqrt(a^2-1)+cosx) Show y`=1/a+cosx Please explain how you got it also!

Answer 1

a=sec(x)

Answer 2

this means \[\sqrt{a^2-1}=\sqrt{sec^2(x)-1}=\sqrt{tan^2(x)}=tan(x)\]

Answer 3

so\[ y=\frac{x}{tan(x)}-\frac{2}{tan(x)}tan^{-1}(\frac{sin(x)}{sec(x)}+tan(x)+cos(x))\]

Answer 4

now that there is only one variable differentiation should be possible