If ^@ cot \theta = \dfrac{ a } { b } ^@ and ^@ 90^\circ > \theta > 0^\circ, ^@ find value of ^@ cosec \theta. ^@


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Answer:

^@ \sqrt{ \dfrac{ b^2 + a^2 } { b^2 } } ^@

Step by Step Explanation:
  1. We know that,
    ^@ cosec \theta = \sqrt{(1 + cot^2\theta)} ^@
  2. Now replace value of ^@ cot\theta ^@ in above equation.
    ^@ cosec\theta = \sqrt{ 1 + \left( \dfrac{ a } { b } \right)^2 } ^@
  3. Simplify ^@ RHS ^@ of above equation.
    ^@ cosec\theta = \sqrt{ \dfrac{ b^2 + a^2 } { b^2 } } ^@

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