Question

$\cot \theta =3x-\frac{1}{12x}\Rightarrow cosec\theta -\cot \theta$ is equal to

• A. $6x$
• B. $\frac{-1}{6x}$
• C. $\frac{1}{6x}$ or $-6x$
• D. $6x$ or $\frac{-1}{6x}$

Answer 1

The correct option is C $\frac{1}{6x}$ or $-6x$

$cot\theta =3x-\frac{1}{12x}$

To find : $cosec\theta -cot\theta$

$1+co{t}^2\theta =cose{c}^2\theta$

$1+(3x{)}^2+(\frac{1}{12x}{)}^2-\frac{1}{2}=cose{c}^2\theta$

$(3x{)}^2+(\frac{1}{12x}{)}^2+\frac{1}{2}=cose{c}^2\theta$

$(3x+\frac{1}{12x}{)}^2=cose{c}^2\theta$

$cosec\theta =\pm (3x+\frac{1}{12x})$

$\Rightarrow cosec\theta -cot\theta$

$=3x+\frac{1}{12x}-3x+\frac{1}{12x}$

$=\frac{1}{6x}$

OR

$\Rightarrow -3x-\frac{1}{12x}-3x+\frac{1}{12x}$

$=-6x$

$cosec\theta -cot\theta =\frac{1}{6x}$ or-6x

option C is correct