Question

if cosec theta=root 5 find the valu of cot theta-cos theta.​

Answer 1

Given that:

• If Cosec Theta = Root 5 .Find The Value Of Cot Theta- Cos Theta

To Find:

• Value Of Cot Theta-Cos Theta

We know that:

• Cosec Theta = Hypotenuse/Opposite Side

Finding The Value Of Cot Theta- Cos Theta:-

↠Cosec Theta = Hypotenuse/Opposite Side

↠√5/1

↠Let: Hypotenuse = √5

↠Opposite Side = 1

↠Adjacent Side = √[(√5)² - 1²]

↠√[4] = 2

Important:-

⇒Cos theta = Adjacent side/Hypotenuse

⇒ Cot theta = Adjacent side/Opposite Side

⇒Cot theta - Cos Theta

➙ 2/1 - 2/√5

➙ (2√5 - 2)/√5

➙ (10 - 2√5)/5

Hence,

Value Of Cot Theta-Cos Theta Is (10 - 2√5)/5

Answer 2

Given ,

$cosec \: θ = \sqrt{5}$

Find ,

$value \: of \: cot \: θ \: - cos \: θ$

we know that ,

$cosec \: θ = \frac{hypotenuse}{perpendicular}$

Solution ,

$cosec \: θ = \frac{ \sqrt{5} }{1}$

Here , H = √5 and P = 1

now ,

${h}^{2} = {p}^{2} + {b}^{2} \\ { \sqrt{5} }^{2} = {1}^{2} + {b}^{2} \\ 5 = 1 + {b}^{2} \\ {b}^{2} = 4 \\ b = 2.$

$cot \: θ = \frac{b}{p} = \frac{2}{1} \\ \\ cos \: θ = \frac{ 2 }{ \sqrt{5} } \\ \\ cot \: θ - cos \: θ = \frac{2}{1} - \frac{2}{ \sqrt{5} } \\ \\ cot \: θ - cos \: θ = 2(1 - \frac{1}{ \sqrt{5} }) .$