Question

If cosec theta - cot theta = root 2 - 1 then let us find the value of (cosec theta + cot theta)​

Answer 1

Answer:

$cosec\theta+cot\theta=\sqrt2+1$

Step-by-step explanation:

Formula used:

$cosec^2A-cot^2A=1$

$a^2-b^2=(a+b)(a-b)$

$cosec\theta-cot\theta=\sqrt2-1$

Taking reciprocals

$\frac{1}{cosec\theta-cot\theta}=\frac{1}{\sqrt2-1}$

Multiply both numerator and denominator by $cosec\theta+cot\theta$

$\frac{cosec\theta+cot\theta}{(cosec\theta-cot\theta)(cosec\theta+cot\theta)}=\frac{1}{\sqrt2-1}$

$\frac{cosec\theta+cot\theta}{cosec^2\theta-cot^2\theta}=\frac{1}{\sqrt2-1}*\frac{\sqrt2+1}{\sqrt2+1}$

$\frac{cosec\theta+cot\theta}{1}=\frac{\sqrt2+1}{{\sqrt2}^2-1^2}$

$\frac{cosec\theta+cot\theta}{1}=\frac{\sqrt{2}+1}{2-1}$

$\implies\:cosec\theta+cot\theta=\sqrt2+1$