Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

Let $\theta =2{\cot }^{-1}7+{\cos }^{-1}(3/5)$. Double-angle addition yields $\cos \theta =44/125$ and $\sin \theta =117/125$. The angle lies in $(0,\pi /2)$, so $\theta ={\cos }^{-1}(44/125)={\cot }^{-1}(44/117)={\csc }^{-1}(125/117)$. Its tangent is $117/44$, not 4/117.