Question

if cosecA+cotA=2+√5 then prove that cosA=2/√5​

Answer 1

Step-by-step explanation:

here is your answer okkkkkkkkkkkkkk

Answer 2

Answer:

proved [your answer is below]

Step-by-step explanation:

given that :cosecA+cotA=2+√5 -------(i)

(cosecA)^2-(cotA)^2=1 [Formulla]

⇨(cosecA+cotA)(cosecA-cotA)=1

⇨cosecA-cotA=1/(cosecA+cotA)

⇨cosecA-cotA=1/2+√5

⇨cosecA-cotA=(2-√5)/(2+√5)(2-√5)

⇨cosecA-cotA=√5-2 ---------(ii)

(i)-(ii)=2cotA=4

⇨cosA/sinA=2 -------(iii)

(i)+(ii)=2cosecA=2√5

⇨sinA=1/√5

By taking the value of sinA to equation (iii):

cosA/1/√5=2

⇨cosA=2/√5 (proved)