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Grade: 12

                        

differentiate tan^-1(√1-x^2)/(√1+x^2) w.r.t cos^-1 x

3 years ago

Answers : (1)

Udita Baranwal
15 Points
							
Let tan^-1{√1+x^2 -√1-x^2 /√1+x^2 + √1-x^2}=u
Let x^2=cos2t  and then
tan u = √1+cos2t - √1-cos2t / √1+cost +√1-cos2t
tan u = √1+2cos^2t-1 - √1-1+2sin^2t / √1+2cos^2t-1 + √1-1+2sin^2t
tan u = cost + sint / cost - sint
Divided by cost 
tan u = 1+tant /1-tant
u= tan^-1{tan(t+π/4)}
u=(t+π/4)
t=1/2 cos^-1 x^2
u=π/4 + 1/2 cos^-1 x^2
du/dx=-x/√1-x^4
Cos^-1 x^2 =v
dv/dx=-2x/√1-x^4
du/dv=du/dx * dx/dv
du/dv=1/2
u=π/4 + 1/2 cos^-1 x^2
du/dx=1/2(-1/√1-x^
2 years ago
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