You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Quotient Rule of Differentiation

If A = tan-1x...

Question

If $A = \tan^{- 1} (x)$ , then $\sin 2 A$ =

$\frac{2 x}{\sqrt{1 - x^{2}}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{2 a}{1 - x^{2}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{2 x}{1 + x^{2}}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$N o n e o f t h e s e$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$\frac{2 x}{1 + x^{2}}$

Finding the value:
Given,
$\begin{array}{rcl} A & = & \tan^{- 1} (x) \\ \tan A & = & x \end{array}$
Also we know,
$s i n 2 A = \frac{2 t a n A}{1 + t a n^{2} A}$
Now put the value of $\tan A = x$
$\sin 2 A = \frac{2 \times x}{1 + x^{2}} \Rightarrow \sin 2 A = \frac{2 x}{1 + x^{2}}$
Hence the correct option is $(B)$

Suggest Corrections

Similar questions

State, Whether the following statements are true of false.

(i) If $a < b, t h e n a - c < b - c$

(ii) If $a > b, t h e n a + c > b + c$

(iii) If $a < b, t h e n a c > b c$

(iv) If $a > b, t h e n \frac{a}{c} < \frac{b}{c}$

(v) If $a - c > b - d; t h e n a + d > b + c$

(vi) If $a < b, a n d c > 0, t h e n a - c > b - c where a, b, c and are real numbers and c \neq 0.$

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

(i) If x ∈ A and A ∈ B, then x ∈ B

(ii) If A ⊂ B and B ∈ C, then A ∈ C

(iii) If A ⊂ B and B ⊂ C, then A ⊂ C

(iv) If A ⊄ B and B ⊄ C, then A ⊄ C

(v) If x ∈ A and A ⊄ B, then x ∈ B

(vi) If A ⊂ B and x ∉ B, then x ∉ A

Q. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x ∈ A and A ∈ B, then x ∈ B (ii) If A ⊂ B and B ∈ C, then A ∈ C (iii) If A ⊂ B and B ⊂ C, then A ⊂ C (iv) If A ⊄ B and B ⊄ C, then A ⊄ C (v) If x ∈ A and A ⊄ B, then x ∈ B (vi) If A ⊂ B and x ∉ B, then x ∉ A

Q. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
(i) If

x \in A

and

A \in B

, then

x \in B

(ii) If

A \subset B

and

B \in C

, then

A \in C

(iii) If

A \subset B

and

B \subset C

, then

A C

(iv) If

A \subset̸ B

and

B \subset̸ C

, then

A \subset̸ C

(v) If

x \in A

and

A \subset̸ B

, then

x \in B

(vi) If

A \subset B

and

x \notin B

, then

x \notin A

Q. If a then b and if b then c

⟹

If a then c.

Join BYJU'S Learning Program

If A=tan-1(x), then sin2A =

The correct option is C 2x1+x2Finding the value:Given, A=tan-1(x)tanA=xAlso we know, sin2A=2tanA1+tan2ANow put the value of tanA=xsin2A=2×x1+x2⇒sin2A=2x1+x2Hence the correct option is(B)

If $A = \tan^{- 1} (x)$ , then $\sin 2 A$ =