If ^@ cot \theta = \dfrac{ a } { b } ^@ and ^@ 90^\circ > \theta > 0^\circ, ^@ find value of ^@ cosec \theta. ^@
Answer:
^@ \sqrt{ \dfrac{ b^2 + a^2 } { b^2 } } ^@
- We know that,
^@ cosec \theta = \sqrt{(1 + cot^2\theta)} ^@ - Now replace value of ^@ cot\theta ^@ in above equation.
^@ cosec\theta = \sqrt{ 1 + \left( \dfrac{ a } { b } \right)^2 } ^@ - Simplify ^@ RHS ^@ of above equation.
^@ cosec\theta = \sqrt{ \dfrac{ b^2 + a^2 } { b^2 } } ^@