Exams › JEE Main › Maths

If the sum of the inverse sine of the series x − x²/2 + x³/4 −... and the inverse cosine of the series x² − x⁴/2 + x⁶/4 −... is equal to π/2, for 0 < |x| < √2, then the value of x is

1. 1/2
2. 1
3. −1/2
4. −1

Correct answer: 1

Solution

The series for the inverse sine converges to arcsin(x) and the series for the inverse cosine converges to arccos(x). Since arcsin(x) + arccos(x) equals π/2 for any x in the interval (0, 1), the correct value of x that satisfies this condition is 1.

Related JEE Main Maths questions

• For the function f(x) = log(x + √(x² + 1)), which of the following describes it correctly?
• For the function f(x) = log((1 + x)/(1 − x)), which of the following relations is satisfied?
• Find the domain of the function f(x)=sin⁻¹{log2(1/2 x²)}.
• For which values of x does the inequality sin⁻¹(sin 5) > x² − 4x hold?
• Determine the range of the function f(x) = sin⁻¹x + tan⁻¹x + sec⁻¹x.
• If A = tan⁻¹ ((x√(3))/(2K-x)) and B = tan⁻¹ ((2x-K)/(K√(3))), then what is the value of A - B?

⚔️ Practice JEE Main Maths free + battle 1v1 →