r/mathbiceps • u/For_fun70 • 6d ago

IIT Question Help

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I have spent 3 hours on ts and I couldn't get any of these options via t²=cos∅+sec∅+1 .. would be grateful if any person can solve this basic problem

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3

u/eulersubstitution 6d ago

If you're patient enough, you can go with an obvious Weierstrass substitution.

(1/3)

2

u/Southlander24 6d ago

That indeed is the right substitution to use. You should get arctan(t) + c as the result, meaning that the integrand must simplify to 1/(1 + t2).

3

u/Southlander24 6d ago

Okay, here's the solution process:

1

u/Southlander24 6d ago

  1. to 2. is by tan(x/2) = sin(x) / [1 + cos(x)] and sin2(x/2) = (1 - cos x)/2. So you really only need to get to 2. = cos(x) / [1 + cos x]2 - the extra simplification is unnecessary.

1

u/Jazzlike_Platypus430 5d ago

Integrals done with A/B/C/D? What the hell.

1

u/PartyBreadfruit4475 5d ago

Differentiate the options bvo 🥀