Solveeit Logo
Login

Question

Mathematics Question on Inverse Trigonometric Functions

The value of tan [cos−1(45)+tan−1(23)]\bigg[cos^{-1}\bigg(\frac{4}{5}\bigg)+tan^{-1}\bigg(\frac{2}{3}\bigg)\bigg] is

A

617\frac{6}{17}

B

176\frac{17}{6}

C

167\frac{16}{7}

D

None of these

Answer

176\frac{17}{6}

Explanation

Solution

tan[cos−1(45)+tan−1(23)]tan\bigg[cos^{-1}\bigg(\frac{4}{5}\bigg)+tan^{-1}\bigg(\frac{2}{3}\bigg)\bigg]
             =tan[tan−1(34)+tan−1(23)]\, \, \, \, \, \, \, \, \, \, \, \, \, =tan\bigg[tan^{-1}\bigg(\frac{3}{4}\bigg)+tan^{-1}\bigg(\frac{2}{3}\bigg)\bigg]
\hspace30mm \bigg[\because \, \, cos^{-1}\bigg(\frac{4}{5}\bigg)=tan^{-1}\bigg(\frac{3}{4}\bigg)\bigg]
             =tab[tan−1(34+231−34.23)]=tan[tan−1(176)]=176\, \, \, \, \, \, \, \, \, \, \, \, \, =tab\Bigg[tan^{-1}\Bigg(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}.\frac{2}{3}}\Bigg)\Bigg] =tan\bigg[tan^{-1}\bigg(\frac{17}{6}\bigg)\bigg]=\frac{17}{6}