Question

sin(tan-1 x), where |x| < 1, is equal to:

(a) x/√(1 – x²)

(b) 1/√(1 – x²)

(c) 1/√(1 + x²)

(d) x/√(1 + x²)

Answer 1

Correct Answer : (d) x / √(1 + x²)

Explanation :

Let tan-1 x = θ

Then, tan θ = x 

From this, we can write the sin θ and cos θ values as:

sin θ = x / √(1 + x²)

cos θ = 1 / √(1 + x²)

Now, consider the given question, 

sin (tan-1 x) = sin θ

                      = x / √(1 + x²)  Since |x| < 1

Therefore, sin(tan-1 x) = x/√(1 + x2).

(d) x/√(1 + x²)