SATHEE: Inverse Circular Functions 1 Question 1

Inverse Circular Functions 1 Question 1

$A \to p; B \to q; C \to p; D \to s$ $A \to p; B \to q; C \to p; D \to s$

1. The number of real solutions of

$\tan^{- 1} \sqrt{x (x + 1)} + \sin^{- 1} \sqrt{x^{2} + x + 1} = \frac{π}{2} is$

(a) zero

(b) one

(d) infinite

Fill in the Blank

Show Answer

Answer:

Correct Answer: 1. (c)

Solution:

Given function is

$\tan^{- 1} \sqrt{x (x + 1)} + \sin^{- 1} \sqrt{x^{2} + x + 1} = \frac{π}{2}$

Function is defined, if

(i) $x (x + 1) \geq 0$ , since domain of square root function.

(ii) $x^{2} + x + 1 \geq 0$ , since domain of square root function.

(iii) $\sqrt{x^{2} + x + 1} \leq 1$ , since domain of $\sin^{- 1}$ function.

From (ii) and (iii), $0 \leq x^{2} + x + 1 \leq 1 \cap x^{2} + x \geq 0$

$\Rightarrow$	$0 \leq x^{2} + x + 1 \leq 1 \cap x^{2} + x + 1 \geq 1$
$\Rightarrow$	$x^{2} + x + 1 = 1$
$\Rightarrow$	$x^{2} + x = 0$
$\Rightarrow$	$x (x + 1) = 0$
$\Rightarrow$	$x = 0, x = - 1$

Inverse Circular Functions 1 Question 1

1. The number of real solutions of

Fill in the Blank

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Inverse Circular Functions 1 Question 1

1. The number of real solutions of

Fill in the Blank

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu