If two angles of a triangle are ${tan}^{- 1} (2) and {tan}^{- 1} (3)$ , then find the third angles

Video Solution

Text Solution

Verified by Experts

Given two angles are ${tan}^{- 1} (2) and {tan}^{- 1} (3)$ . Now $(2) (3) > 1$
$\Rightarrow {tan}^{- 1} (2) and {tan}^{- 1} (3) = π + {tan}^{- 1} (\frac{2 + 3}{1 - 2 \times 3})$
$= π + {tan}^{- 1} = π - \frac{π}{4} = \frac{3 π}{4}$
Hence, the third angle is $π - \frac{3 π}{4} = \frac{π}{4}$

|

Updated on:21/07/2023

Class 12 MATHS INVERSE TRIGONOMETRIC FUNCTIONS

Related Playlists

Knowledge Check

Question 1 - Select One
Two angles of a triangle are ${tan}^{- 1} \frac{1}{2} and {tan}^{- 1} \frac{1}{3}$ . What is the third angle ?
A $30^{\circ}$
B $45^{\circ}$
C $90^{\circ}$
D $135^{\circ}$
Question 1 - Select One
If two angles of a triangle are ${cot}^{- 1} 2$ and ${cot}^{- 1} 3$ , then the third angle is
A $\frac{π}{4}$
B $\frac{3 π}{4}$
C $\frac{π}{6}$
D $\frac{π}{3}$
Question 1 - Select One
Two angles of a triangle are ${sin}^{- 1} (1 / \sqrt{5})$ and ${sin}^{- 1} (1 / \sqrt{10})$ then the third angle is
A $π / 4$
B $3 π / 4$
C $π / 6$
D $π / 3$

Similar Questions

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Question Bank

Home
Ask Doubt
Profile