Question:

$Let \tan α = \frac{a}{a + 1} and \tan β = \frac{1}{2 a + 1} then α + β is$

WBJEE

Updated On: Feb 15, 2024

(A) π/4
(B) π/3
(C) π/2
(D) π

Hide Solution

Verified By Collegedunia

The Correct Option is A

Solution and Explanation

Explanation:

\tan α = \frac{a}{a + 1}, \tan β = \frac{1}{2 a + 1}

\tan (α + β) = \frac{\frac{a}{a + 1} + \frac{1}{2 a + 1}}{1 - \frac{a}{(a + 1) (2 a + 1)}} = \frac{\frac{a (2 a + 1) + a + 1}{(a + 1) (2 a + 1)}}{\frac{(a + 1) (2 a + 1) - a}{(a + 1) (2 a + 1)}} = \frac{2 a^{2} + 2 a + 1}{2 a^{2} + 2 a + 1} = 1

α + β = \frac{π}{4}

Was this answer helpful?

0

0

Top Questions on Trigonometric Identities

Let \(\frac{\pi}{2}<x<\pi\) be such that \(\cot x=\frac{-5}{\sqrt{11}}\). Then
\((\sin\frac{11x}{2})(\sin 6x-\cos6x)+(\cos\frac{11x}{2})(\sin 6x+\cos 6x)\)
is equal to
- JEE Advanced - 2024
- Mathematics
- Trigonometric Identities
View Solution
Prove that: \[ \frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta \]
- CBSE Class X - 2024
- Mathematics
- Trigonometric Identities
View Solution
If $\sin A = \frac{3}{5}$ and $\cos B = \frac{12}{13}$, then find the value of $(\tan A + \tan B)$.
- CBSE Class X - 2024
- Mathematics
- Trigonometric Identities
View Solution
If $\tan \theta + \sec \theta = m$, then prove that $\sec \theta = \frac{m^2 + 1}{2m}$.
- CBSE Class X - 2024
- Mathematics
- Trigonometric Identities
View Solution
If tan A = 3 cot A, then the measure of the angle A is :
- CBSE Class X - 2024
- Mathematics
- Trigonometric Identities
View Solution

View More Questions

Questions Asked in WBJEE exam

View More Questions