cosec18[^] is a root of the equation :

Question

cosec18$$^\circ$$ is a root of the equation :

Accepted Answer

$$\cos ec18^\circ  = {1 \over {\sin 18^\circ }} = {4 \over {\sqrt 5  - 1}} = \sqrt 5  + 1$$

Let $$\cos ec18^\circ  = x = \sqrt 5  + 1$$

$$ \Rightarrow x - 1 = \sqrt 5 $$

Squaring both sides, we get

${x^2} - 2x + 1 = 5$

$$ \Rightarrow {x^2} - 2x - 4 = 0$$

Solutions · 1