Question

7. If y = tan-'[{/(1 + x 2) - 13/x], then​

Answer 1

Answer:

Given y = tan-1 √(a – x)/(a + x)

Put x = a cos 2θ

θ = ½ cos-1 (x/a)

So y = tan-1 √(a – a cos 2θ)/(a + a cos 2θ)

= tan-1 √a(1 – cos 2θ)/a(1 + cos 2θ)

= tan-1 √(2 sin2θ)/(2cos2θ)

= tan-1 tan θ

= θ

= ½ cos-1 (x/a)

Differentiate w.r.t.x

dy/dx = (½)× [-1/√(1 – (x/a)2) ] ×(1/a)

= -1/2√(a2 -x2)