Question

Ifcosec √5;find the value of cot cos (where theta is acute

Answer 1

cosec Ф = √5
sin Ф = 1/cosec Ф = 1/√5

we know that sin² Ф + cos² Ф = 1
⇒cos² Ф = 1 - sin² Ф
⇒cos Ф = √(1 - sin² Ф)

⇒cos Ф = $\sqrt{1- (\frac{1}{ \sqrt{5} } })^{2} = \sqrt{1- \frac{1}{5} } = \sqrt{ \frac{4}{5} } = \frac{2}{ \sqrt{5} }$

⇒cos Ф = $\frac{2}{ \sqrt{5} }$

cot Ф = cos Ф / sin Ф = $\frac{2/ \sqrt{5} }{1/ \sqrt{5} } = 2$

Answer 2

If coesc Ф=√5,then hypotenuse =√5and opp side=1and adjacent side=2
cotФ=2,cosФ=2/√5
cotФ*cosФ=2*2/√5=4/√5