prove that : _________1_________ = 1+cos(theta)
cosec(theta)+ cot(theta) sin(theta)

please answer quickly

Dear Student,

Please find below the solution to the asked query :
$$\begin{gathered} \mathrm{Although} \mathrm{RHS} \mathrm{is} \mathrm{not} \mathrm{clear}, \mathrm{so} \mathrm{taking} \mathrm{LHS}\hspace{0.17em}\mathrm{and} \mathrm{simplifying}, \\ \frac{1}{\mathrm{cosec\theta }+\mathrm{cot\theta sin\theta }}= \frac{1}{\mathrm{cosec\theta }+{\displaystyle \frac{\mathrm{cos\theta }}{\mathrm{sin\theta }}}\times \mathrm{sin\theta }} \\ =\frac{1}{\mathrm{cosec\theta }+\mathrm{cos\theta }}=\frac{\mathrm{sin\theta }}{1+\mathrm{sin\theta cos\theta }} \end{gathered}$$


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