If sin theta=1/3then find the value of 2cot^2+2
if sin theta=1/3, then
sin^2+cos^2=1
cosTheta=sqrt(1-sin^2)=sqrt(8/8)
= 2sqrt2 /3
and ctnTheta=cos/sin= 2sqrt2
then 2 ctn^2+2= ..... 18?
if sinθ = 1/3,
2cot^2θ + 2 = 2csc^2θ = 2(3)^2 = 18
= (9)+(224)
= 233
To find the value of 2cot^2θ + 2, we need to determine the value of cot θ or cotangent θ.
Given that sin θ = 1/3, we can use the Pythagorean identity to find the value of cos θ.
The Pythagorean identity is:
sin^2θ + cos^2θ = 1
Substituting the given value of sin θ:
(1/3)^2 + cos^2θ = 1
1/9 + cos^2θ = 1
cos^2θ = 1 - 1/9
cos^2θ = 8/9
cos θ = ±√(8/9)
Since sin θ is positive, we can ignore the negative sign.
cos θ = √(8/9)
Now, we can calculate cot θ using the definition of cotangent:
cot θ = cos θ / sin θ
cot θ = (√(8/9)) / (1/3)
cot θ = √(8/9) * (3/1)
cot θ = 3√(8/9)
Finally, we can substitute this value into the expression 2cot^2θ + 2:
2(3√(8/9))^2 + 2
2(9/9)(8/9) + 2
2(72/81) + 2
144/81 + 2
16/9 + 2
18/9 + 2
2 + 2
4
Therefore, the value of 2cot^2θ + 2 is 4.