Question

cot theta+tan theta=x​

Answer 1

${\large{\underbrace{\textsf{\textbf{\color{red}{➵}{\color{green}{\:\:αηѕωєя\: :-}}}}}}}$

Solution :

$\rm\begin{gathered} \implies \sin \theta\times \cos \theta\times \tan\theta \times \csc\theta \times \sec\theta \times \cot\theta \\ \\ \implies \sin \theta \times \cos\theta \times \frac{ \cancel{\sin\theta}}{ \cos\theta} \times \frac{1}{ \cancel{\sin\theta}} \times \frac{1}{\cancel{ \cos\theta}} \times \frac{ \cancel{\cos\theta}}{ \sin\theta} \\ \\\implies\cancel{ \sin\theta } \times \cancel{\cos\theta} \times \frac{1}{ \cancel{\cos\theta}} \times \frac{1}{\cancel{\sin\theta}} \\ \\\implies1 \times 1 \times 1 \times 1\\ \\ \implies1 \end{gathered}$

Identity used :

• $\begin{gathered}\large \tan\theta = \frac{ \sin\theta}{ \cos\theta} \\ \\ \large\cot \theta = \frac{ \cos\theta}{ \sin\theta} \\ \\ \large \csc \theta= \frac{1}{ \sin\theta} \\ \\\large \sec \theta= \frac{1}{ \cos\theta} \end{gathered}$