If cotθ=1/√(x) 3\\ , the value of sec^(2) θ + cosec^(2) θ is a) 1 b) 40/9 c) 38/9 d) 5(1)/(3)

Question

If cotθ=1/
`√(x) 3\\` , the value of
`sec^(2)` θ +
`cosec^(2)` θ is

a) 1
b) 40/9
c) 38/9
d) 5
`(1)/(3)`

Answer 1

`\text{Given that,}~\\\\\cot \theta = \frac 1{\sqrt 3} \\\\\\\text{So,}~~ \tan \theta = \frac 1{\cot \theta} = \sqrt 3\\\\\\\sec^2 \theta + \csc^2 \theta \\\\=(1+\tan^2 \theta) + (1 + \cot^2 \theta)\\\\=1 +\left (\sqrt 3 \right)^2 + 1 + \left(\frac 1{\sqrt 3} \right)^2\\\\=1 +3 + 1 + \frac 13 \\\\= 5 + \frac 13 \\\\= 5 \frac 13`