plzzz give me answer .............
Answers
LHS=
1−cosθ
tanθ
+
1−tanθ
cotθ
=
1−cotθ
tanθ
+
1−
cotθ
1
cotθ
\begin{lgathered}=\frac{tan{\theta}}{1-cot{\theta}}-\frac{cot^2{\theta}}{1-cot{\theta}} \\\end{lgathered}
=
1−cotθ
tanθ
−
1−cotθ
cot
2
θ
\begin{lgathered}=\frac{\frac{1}{cot{\theta}}-cot^2{\theta}}{1-cot{\theta}} \\\end{lgathered}
=
1−cotθ
cotθ
1
−cot
2
θ
\begin{lgathered}=\frac{1-cot^3{\theta}}{cot{\theta}(1-cot{\theta})} \\\end{lgathered}
=
cotθ(1−cotθ)
1−cot
3
θ
\begin{lgathered}=\frac{(1-cot{\theta})(1+cot^2{ \theta}+cot{\theta})}{cot{\theta}(1-cot{\theta})} \\\end{lgathered}
=
cotθ(1−cotθ)
(1−cotθ)(1+cot
2
θ+cotθ)
\begin{lgathered}=\frac{1}{cot{\theta}}+\frac{cot^2{\theta}}{cot{\theta}}+\frac{cot{\theta}}{cot{\theta}} \\\end{lgathered}
=
cotθ
1
+
cotθ
cot
2
θ
+
cotθ
cotθ
= tan{\theta}+cot{\theta}+1=RHS=tanθ+cotθ+1=RHS