Question

What's my mistake and why my answer is different than what it should be ? ​

Answer 1

Answer: i think it may be in the third step.

Step-by-step explanation:

I suggest doing it all over again. Trigonometry always tends to confuse us.

Answer 2

y = sin⁻¹(2x/1 + x²)

Substitute x = tan∅ => ∅ = tan⁻¹x

=> y = sin⁻¹(2x/1 + x²)

=> y = sin⁻¹(2tan∅/1 + tan²∅)

=> y = sin⁻¹(sin 2∅)

=> y = 2∅

=> y = 2tan⁻¹x

On differentiating with respect to x, we get

=> dy/dx = d/dx(2 tan⁻¹x)

=> dy/dx = 2[d/dx(tan⁻¹x)]

=> dy/dx = 2(1/1 + x²)

=>  dy/dx = (2/1 + x²)

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