Show that the substitution = 2 tan 1 t (Figure 2) yields the formulas This substitution

Show that the substitution θ = 2 tan⁻¹ t (Figure 2) yields the formulas

This substitution transforms the integral of any rational function of cos θ and sin θ into an integral of a rational function of t (which can then be evaluated using partial fractions). Use it to evaluate

Transcribed Image Text:

Cos 0 = 1-1² 1 + f²' sin 0: 21 1 + f²' de = 2 dt 1 + f²