Question

if cosec a=2 find the value of sina/1+cosA​

Answer 1

Step-by-step explanation:

Given:-

Cosec A = 2

To find:-

Find the value of Sin A / (1+Cos A) ?

Solution:-

Given that

Cosec A = 2 -------(1)

=> 1 / Sin A = 2

=> Sin A = 1/2------(2)

On squaring both sides then

=> Sin^2 A = (1/2)^2

=> Sin^2 A = 1/4

=> 1- Sin^2 A = 1-(1/4)

=> 1-Sin^2 A = (4-1)/4

=> 1-Sin^2 A = 3/4

We know that

Sin^2 A + Cos^2 A = 1

=> Cos^2 A = 3/4

=>Cos A =√(3/4)

(On taking positive value)

=> Cos A = √3/2---------(3)

Now,

Sin A / (1+Cos A)

From (1),(2)&(3)

=> (1/2)/[1+(√3/2)]

=>(1/2)/[2+√3)/2]

=> (1/2)×[2/(2+√3)]

=>(1×2)/(2×(2+√3))

=>1/(2+√3)

Answer:-

The value of Sin A / (1+Cos A) for the given problem is 1/(2+√3)

Used formulae:-

• Cosec A = 1/Sin A

• Sin^2 A + Cos^2 A = 1