Question

prove that tan inverse X +tan inverse[2x/1-x square]=tan inverse[3x-x cube/1-3x square],|x|

Answer 1

Answer:

I dont no this answered by his

Answer 2

$\large{\underline{\mathfrak{Proof:-}}}$

let x = tan ∅

Then ∅ = tan-¹ x

we have

RHS = tan-¹ (3x-x³/1-3x²)

= tan-¹(3tan∅-tan³∅/1-3tan²∅)

= tan-¹(tan3∅)

= 3∅

= 3tan-¹ x

= tan-¹ x + 2tan-¹ x

= tan-¹x + tan-¹ 2x/1-x² = LHS

$\large{\underline{\mathfrak{Related\: Formulas:-}}}$

• tan-¹x + tan-¹ y = tan-¹(x+y/1-xy)

• 2tan-¹ x = sin-¹ 2x/1+x²

• 2 tan-¹x = cos-¹ 1-x²/1+x²

• 2 tan-¹ x= tan-¹ 2x/1-x²

• sin-¹x + cos -¹ x = π/2

• tan-¹ x + cot-¹x = π/2

cosec-¹x + sec-¹ x = π/2