If X= cot − 1 ( cos α ) − tan − 1 ( cos α ) , with cos α ≥ 0 , find sin X.

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsProperties of ITFMedium2 minQB

MathematicsMediumsingle choice

If X= $cot^{- 1} (cos α) - tan^{- 1} (cos α)$ , with cos $α \geq 0$ , find sin X.

Answer:

Solution:

For t= $cos α$ , $sin (cot^{- 1} t - tan^{- 1} t) = (1 - t^{2}) / (1 + t^{2}) = (1 - cos α) / (1 + cos α) = tan^{2} (α /2)$ .

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Properties of ITF

⏱ 2mℹ️ Source: QB

Loading discussions...