Question:
The solution of $\tan 2\theta\: \tan \theta = 1$ is
The solution of $\tan 2\theta\: \tan \theta = 1$ is
Updated On: Aug 25, 2023
- $\frac{\pi}{3}$
- $(6n\pm1)\frac{\pi}{6}$
- $(4n\pm1)\frac{\pi}{6}$
- $(2n\pm1)\frac{\pi}{6}$
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The Correct Option is B
Solution and Explanation
\(\tan\,2 \theta \,\tan\,\theta=1\)
\(\tan3\theta=\frac{\tan\theta+\tan2\theta}{1-\tan\theta.\tan2\theta}\)
\(\tan3\theta=\)∞
i,e, \(3\theta=\frac{2n+1}{2}\pi\)
\(\theta=\frac{{(2n+1)}}{6}\pi\)
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Concepts Used:
Integral
The representation of the area of a region under a curve is called to be as integral. The actual value of an integral can be acquired (approximately) by drawing rectangles.
- The definite integral of a function can be shown as the area of the region bounded by its graph of the given function between two points in the line.
- The area of a region is found by splitting it into thin vertical rectangles and applying the lower and the upper limits, the area of the region is summarized.
- An integral of a function over an interval on which the integral is described.
Also, F(x) is known to be a Newton-Leibnitz integral or antiderivative or primitive of a function f(x) on an interval I.
F'(x) = f(x)
For every value of x = I.
Types of Integrals:
Integral calculus helps to resolve two major types of problems:
- The problem of getting a function if its derivative is given.
- The problem of getting the area bounded by the graph of a function under given situations.