Question

1 + cot square theta by cosec theta equal to cosec theta ​

Answer 1

Answer:

$\displaystyle\mathrm{Prove\:}\frac{1+\cot ^2\left(\theta\right)}{\csc \left(\theta\right)}=\csc \left(\theta\right):\quad \mathrm{True}$

Step-by-step explanation:

$\dfrac{1+\cot ^2\left(\theta\right)}{\csc \left(\theta\right)}=\csc \left(\theta\right)$

$\gray{\mathrm{Manipulating\:left\:side}}$

$\gray{\dfrac{1+\cot ^2\left(\theta\right)}{\csc \left(\theta\right)}}$

$\gray{\mathrm{Use\:the\:following\:identity}:\quad \:1+\cot ^2\left(x\right)=\csc ^2\left(x\right)}$

$=\dfrac{\csc ^2\left(\theta\right)}{\csc \left(\theta\right)}$

$\gray{\mathrm{Refine}}$

$=\csc \left(\theta\right)$

$\gray{\mathrm{We\:showed\:that\:the\:two\:sides\:could\:take\:the\:same\:form}}}$

$\Rightarrow \mathrm{True}$