Edugain

Login/Register Edugain for School

• Indonesia

Simplify $\sqrt { \dfrac { 1 + cos \theta } { 1 - cos \theta } }$.

1. Home
2. Math
3. All Questions

Answer:

$cosec \theta + cot \theta$

Step by Step Explanation:

1. We know that $1 - cos^2 \theta = sin^2 \theta$. Using this identity we can simplify the denominator by multiplying it by $1 + cos \theta$.
2. Now, on multiplying numerator and denominator by $1 + cos \theta$,
   $\begin{align} \sqrt { \dfrac { 1 + cos \theta } { 1 - cos \theta } } & = \sqrt { \dfrac { 1 + cos \theta } { 1 - cos \theta } \times \dfrac { 1 + cos \theta } { 1 - cos \theta } } \\ & = \sqrt { \dfrac { (1 + cos \theta)^2 } { 1 - cos^2 \theta } } \\ & = \sqrt { \dfrac { (1 + cos \theta)^2 } { sin ^2 \theta } } \\ & = \dfrac { 1 + cos \theta } { sin \theta } \\ & = \dfrac { 1 } { sin \theta } + \dfrac { cos \theta } { sin \theta } \\ & = cosec \theta + cot \theta \end{align}$

Practice online or create unlimited worksheets on similar questions.

You can reuse this answer
Creative Commons License