1. Tardigrade
  2. Question
  3. Mathematics
  4. The value of sin (4 tan -1 (1/3))- cos (2 tan -1 (1/7)) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The value of $\sin \left(4 \tan ^{-1} \frac{1}{3}\right)-\cos \left(2 \tan ^{-1} \frac{1}{7}\right)$ is

Inverse Trigonometric Functions

Solution:

$ \sin \left(4 \tan ^{-1} \frac{1}{3}\right)=2 \sin \left(2 \tan ^{-1} \frac{1}{3}\right) \cos \left(2 \tan ^{-1} \frac{1}{3}\right)$
$=2 \sin \left(\tan ^{-1} \frac{3}{4}\right) \cos \left(\tan ^{-1} \frac{3}{4}\right)=2 \cdot \frac{3}{5} \cdot \frac{4}{5}=\frac{24}{25}$
$\cos \left(2 \tan ^{-1} \frac{1}{7}\right)=\cos \left(\tan ^{-1} \frac{7}{24}\right)=\frac{24}{25}$
The given expression $= 0 $