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The value of tan ^-12-tan ^-11/3 is Single correct option
The value of
tan − 1 2 − tan − 1 1 3 \tan^{-1}2-\tan^{-1}\dfrac13 tan − 1 2 − tan − 1 3 1 is
A. π 4 \dfrac\pi4 4 π B. π 3 \dfrac\pi3 3 π C. π 2 \dfrac\pi2 2 π D. tan − 1 5 3 \tan^{-1}\dfrac53 tan − 1 3 5 Show answer and solution Answer: (A) π 4 \dfrac\pi4 4 π
Use
tan − 1 a − tan − 1 b = tan − 1 a − b 1 + a b \tan^{-1}a-\tan^{-1}b=\tan^{-1}\dfrac{a-b}{1+ab} tan − 1 a − tan − 1 b = tan − 1 1 + ab a − b , valid since
a b > − 1 ab>-1 ab > − 1 . Here
2 − 1 3 1 + 2 3 = 5 / 3 5 / 3 = 1 \dfrac{2-\frac13}{1+\frac23}=\dfrac{5/3}{5/3}=1 1 + 3 2 2 − 3 1 = 5/3 5/3 = 1 , so the value is
tan − 1 1 = π 4 \tan^{-1}1=\dfrac\pi4 tan − 1 1 = 4 π . The option
tan − 1 5 3 \tan^{-1}\dfrac53 tan − 1 3 5 is the numerator alone, a result of forgetting the denominator
1 + a b 1+ab 1 + ab .
Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake