Solve for x: ^ -1 3x + ^ -1 2x = 4 - Vidyadip

Question

$\text{Solve for x:} \tan^{-1} 3x + \tan^{-1} 2x = \frac{ \pi}{4}$

✓

Answer

$\tan^{-1} 3x + \tan^{-1} 2x = \frac{\pi}{4} \Rightarrow \tan^{-1}\bigg(\frac{5x}{1 - 6x^{2}}\bigg) = \frac{\pi}{4}$$\Rightarrow \frac{5x}{1 - 6x^{2}} = 1 \Rightarrow 6x^{2} + 5x - 1 = 0$
$\text{Solving to get x} = -1, \text{x} = \frac{1}{6} $
$\text{x} = -1 \text{does not satisfy the equation,} \therefore \text{x} = \frac{1}{6} \text{is the solution}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the second order derivatives of the following functions:$\sin(\log\text{x})$

Find the derivative of the function f defined by f(x) = mx + c at x = 0.

Prove the following:
$\tan^{-1}\sqrt{x}=\frac{1}{2}\cos^{-1}\Bigg(\frac{1-x}{1+x}\Bigg),\text{x }\epsilon(0, 1)$.

Find the intervals in which f(x) is increasing or decreasing:
$\text{f}(\text{x})=\sin\text{x}+|\sin\text{x}|,0<\text{x}\leq2\pi$

Assume that the chances of a patient having a heart attack is $40\%. $ It is also assumed that a meditation and yoga course reduce the risk of heart attack by $30\%$ and prescription of certain drug reduces its chances by $25\%$. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

If $\text{y}=\cos^{-1}\text{x},$ Find $\frac{\text{d}^2\text{y}}{\text{dx}^2}$ in terms of y alone.

If $\text{y}=\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big),$ write the value of $\frac{\text{dy}}{\text{dx}}\text{ for x}>1.$

A die is thrown three times. Find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ and $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$, if
A = 4 appears on the third toss,
B = 6 and 5 appear respectively on first two tosses.

Differentiate the following w.r.t. x:
$(\sin\text{x})^{\cos\text{x}}$

Solve the following differential equations:
$\text{xy}\frac{\text{dy}}{\text{dx}}=1+\text{x + y + xy}$